Class 10th Mathematics Gujarat Board Solution
Exercise 10- A pole stands vertically on the ground. If the angle of elevation of the top of…
- A string of a kite is 100 m long and it makes an angle of measure 60 with the…
- A circus artist is climbing from the ground along a rope stretched from the top…
- A tree breaks due to a storm and the broken part bends such that the top of the…
- An electrician has to repair an electric fault on the pole of height 5 m. He…
- As observed from a fixed point on the bank of a river, the angle of elevation…
- As observed from the top of a hill 200 m high, the angles of depression of two…
- A person standing on the bank of a river, observes that the angle subtended by…
- The shadow of a tower is 27 m, when the angle of elevation of the sun has…
- From a point at the height 100 m above the sea level, the angles of depression…
- From the top of a 300 m high light - house, the angles of depression of the…
- As observed from a point 60 m above a lake, the angle of elevation of an…
- Watching from a window 40 m high of a multi - storeyed building, the angle of…
- Two pillars of equal height stand on either side of a road, which is 100 m…
- The angles of elevation of the top of a tower from two points at distance a…
- A man on the top of a vertical tower observes a car moving at a uniform speed…
- If the angle of elevation of a cloud from a point h metres above a lake has…
- From the top of a building vector ab , 60 m high, the angles of depression of…
- A bridge across a valley is h metres long. There is a temple in the valley…
- At a point on level ground, the angle of elevation of a vertical tower is…
- A statue 1.46 m tall, stands on the top of a pedestal. From the point on the…
- On walking ……….. metres on a hill making an angle of measure 30 with the…
- The angle of elevation of the top of the tower from a point P on the ground…
- A 3 m long ladder leans on the wall such that its lower end remains 1.5 m…
- A tower is 50√3 m high. The angle of elevation of its top from a point 50 m…
- If the ratio of the height of a tower and the length of its shadow is 1 : √3,…
- If the angles of elevation of a tower from two points distance a and b (a b)…
- The tops of two poles of height 18 m and 12 m are connected by a wire. If the…
- The angle of elevation of the top of the building A from the base of building…
- If the angle of elevation of the top of a tower of a distance 400 m from its…
- The angle of depression of a ship from the top of a tower 30 m height has…
- When the length of the shadow of the pole is equal to the height of the pole,…
- From the top of a building h metre high, the angle of depression of an object…
- As observed from the top of the light house the angle of depression of the…
- Two poles are x metres apart and the height of one is double than that of the…
- A pole stands vertically on the ground. If the angle of elevation of the top of…
- A string of a kite is 100 m long and it makes an angle of measure 60 with the…
- A circus artist is climbing from the ground along a rope stretched from the top…
- A tree breaks due to a storm and the broken part bends such that the top of the…
- An electrician has to repair an electric fault on the pole of height 5 m. He…
- As observed from a fixed point on the bank of a river, the angle of elevation…
- As observed from the top of a hill 200 m high, the angles of depression of two…
- A person standing on the bank of a river, observes that the angle subtended by…
- The shadow of a tower is 27 m, when the angle of elevation of the sun has…
- From a point at the height 100 m above the sea level, the angles of depression…
- From the top of a 300 m high light - house, the angles of depression of the…
- As observed from a point 60 m above a lake, the angle of elevation of an…
- Watching from a window 40 m high of a multi - storeyed building, the angle of…
- Two pillars of equal height stand on either side of a road, which is 100 m…
- The angles of elevation of the top of a tower from two points at distance a…
- A man on the top of a vertical tower observes a car moving at a uniform speed…
- If the angle of elevation of a cloud from a point h metres above a lake has…
- From the top of a building vector ab , 60 m high, the angles of depression of…
- A bridge across a valley is h metres long. There is a temple in the valley…
- At a point on level ground, the angle of elevation of a vertical tower is…
- A statue 1.46 m tall, stands on the top of a pedestal. From the point on the…
- On walking ……….. metres on a hill making an angle of measure 30 with the…
- The angle of elevation of the top of the tower from a point P on the ground…
- A 3 m long ladder leans on the wall such that its lower end remains 1.5 m…
- A tower is 50√3 m high. The angle of elevation of its top from a point 50 m…
- If the ratio of the height of a tower and the length of its shadow is 1 : √3,…
- If the angles of elevation of a tower from two points distance a and b (a b)…
- The tops of two poles of height 18 m and 12 m are connected by a wire. If the…
- The angle of elevation of the top of the building A from the base of building…
- If the angle of elevation of the top of a tower of a distance 400 m from its…
- The angle of depression of a ship from the top of a tower 30 m height has…
- When the length of the shadow of the pole is equal to the height of the pole,…
- From the top of a building h metre high, the angle of depression of an object…
- As observed from the top of the light house the angle of depression of the…
- Two poles are x metres apart and the height of one is double than that of the…
Exercise 10
Question 1.A pole stands vertically on the ground. If the angle of elevation of the top of the pole from a point 90 m away from the pole has measure 30, find the height of the pole.
Answer:Suppose AB represents the pole. C is a point 90m away from the pole.
![](data:image/png;base64,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)
AB = Height of the pole
BC = 90m
∠B is a right angle in ∆ABC and ∠C = 30⁰
In ∆ABC,
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEsAAAAuCAMAAABXqRQxAAAAAXNSR0IArs4c6QAAAJlQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOjoAOjpmOjqQOmaQOma2OpDbZgAAZgA6ZgBmZjoAZjo6ZjqQZpCQZpDbZrbbZrb/kDoAkDo6kDpmkGYAkGY6kLaQkLbbkNv/tmYAtmY6tpA6ttv/tv/btv//25A627Zm27aQ29u229v/2////7Zm/9uQ/9u2/9vb//+2///bXN+orAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAACB0lEQVRIS+1W21LCQAztci2CVvFGVYRVcKnQlt3//zhz6W1nKu0CD45DHgqddk+Sk9MknvfnLbpfusRowsEO3jehQOtc401m6VR0v1ywYtEh3zoYAuKngGtmyWSl3LDko3+Dh02IKDqgKHNzw9J36zxJxirjgls3LDXMDlBc+7e+RZATlglnXuLPCvIHK4trJ6xkvMuYoriM5EIcxZciJWC1TuZe32IYsYAkGcuElgpccoxJASytWk3YKR/SLZ8HLAiGAaUgsZGZuQ/5954OIRTPdCAEBIY/3TV/Q73nVicvL10YsBmQJB9qw9bXW8dT8ar1p4HRow6dt0ouOZ7Xc9ELKyyc6MG8NNaptQf9UB1wjceiqRB9GhhmLsTYHh2xNeCasFRnAQ2Q+/1gl9od2pPYuzcj8NYiVx1gG6VrjBqmzl821lfwIcFbGjYLvBiN0F0pOHts48DzJOapLB/1yXJcmB6vO/Y6oYreT46aTHaXuNzkWNkC5e23ePAjYymdT+ya1KNi8frvMIIYha/pnDYnfUfB4GiZtNZGAltTniOCfG8pp1IRkd8mR4pWYZUy7pkiRPdUWdO4MjYP0sbFo1LlmsBVoPoBEXYLi3zaUbGEOfUESoqA3BHF1t1voIl/teBnsOmWHAPqJls9gYCUV8djTYkR05XiVlHdrt0RaV85l8Ei+4/tB9jfMOE2OQ04AAAAAElFTkSuQmCC)
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![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGoAAAAXCAMAAADUQyq6AAAAAXNSR0IArs4c6QAAAIdQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOjpmOjqQOmaQOma2OpDbZgAAZgA6ZgBmZjoAZjo6ZpCQZpDbZrbbZrb/kDoAkDo6kGYAkGY6kLaQkLbbkNv/tmYAtpA6ttv/tv/btv//25A625Bm27aQ2////7Zm/9uQ/9u2/9vb//+2///bR+aSFAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABiUlEQVRIS+1U2XaCMBBNXGNVWm2F1mqKRQVK/v/7OktCgi0oD32q85BzCJO53IUIca//ocBx35enSSZnOGMSiTVY4MOVKhS1MtRp7SFPKynHaevp3J6poikAfkhYr1WhYtdSruTw0z1kg50w2j9fztHPaol7JkGQKiKO3eWhinma1aOrCAfx+ltVTwenIEP1YyWEh+IvsIaIXMr4qORC0IKVTW0zsfp6G9dytDMLBAyhmI+DEoWa7UUmZzuRka0miWGPvwa9njRM1RSVIAMMD0OUHNs0eFZCD/fotrWAxhboDgMUD2frErEy2uaq0yzzuhFlYjsDKLOFAL47CywU4SFURt+MzvaIhaXG9gdQjX0G8Ev1iDLkEjYZyiRhVlsEpJEuQJdQbAzJ3IDKSVf+pW4Pu0Y+5MJPVj7CTSgeD1BAhfG0bPsrAvfQ0NLRZxYO4aTq64a0srFYiggid4Y2cOvAF9No0xkIflmuoXOeot5bvKNGLxYKorlz5/H2iuvlhqn3lrsCf6jANyrNI3yEXZMSAAAAAElFTkSuQmCC)
Thus, the height of the pole is 51.9 m.
Question 2.A string of a kite is 100 m long and it makes an angle of measure 60 with the horizontal. Find the height of the kite, assuming that there is no slack in the string.
Answer:Let PR be the string of a kite P and QR be the horizontal direction.
![](data:image/png;base64,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)
PR = 100 m
∠PQR = 90⁰
∠PRQ = 60⁰
PQ = Height of the kite
In ∆PQR,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIYAAAAvCAMAAAARtEKFAAAAAXNSR0IArs4c6QAAAJZQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOgA6OjoAOjpmOjqQOmaQOma2OpDbZgAAZgBmZjoAZjo6ZjpmZjqQZmaQZpDbZrbbZrb/kDoAkDo6kDpmkGY6kLbbkNv/tmYAtmY6tpA6tpBmttv/tv//25A627Zm27aQ29u229v/2////7Zm/9uQ/9u2/9vb//+2///bligmHQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAChElEQVRYR+1XYXPTMAy1ytZmYx2lDBiBQoDNbZfExP//zyHJThwnu1tql7rHTR9a586SnqQn2RbiVf67DEhwki44/fVHOufOc/OxPAcY1eIcUIjiixB6ew1wOaU4uw9ml94A3Dz4q5hw9LdHIYrZd6Hy2Ys41Bre4HZEkc9LldParWJQiPoGqVFQYSRgXlpp7tidUPafP+rlgzQwKoJckYJbRcGQ71r1wngwovNL+mpWt751C4P3NitE71aBMP48keJPWwm1WXKpHY55aRx5YmBQJQjGvHSrMBRqA+Siec8paFYAS79x0cF+vRg2cx8GQTAwzG+I7J84na5dd1m/KBwyjI0fGwYSLkNaSEfLCjqaWHq8AINK1hYlfPhobLj+JGdYHjn261E6fIqigqWoH8FB5cGG43bFkMgK99+IooOaWxjc3KzgVgf59j1tOQpNk0t5NLOkG7WKNDPOb5JwhjIaCdcmAWqTAdz2A1efzFdt/w1baBtcfCaNddtabhWajmY1aI5QQ5F6MpzgY8/Y4CRveQruMFsX95HwwtSZSGb8yNm90L8GEyDM6sFaOm9PSNP7zPzTi4FBU7Aw/ocD8TSQumzQYOQ2y47JvalBMIxdNi9pqpCSP3WK7gHwb2vFrTLD8fM8jGej6T1OjrJkStoanEFROOaOov1T6nRFaRlpW8S7Vk5lWPS+HiML4PHVT0a0+YkGiKHt/UT/xkNw0sNnovHgbTV2brCyp6jpgAqOqYJFqehSECtUYRV+Gdhm/h0mFM74MRdqKV7Pv6LG2wu0kKb5h2DrLEXzD1GYt0Nq6U6rtECK0Vs6BR5Jg7BKXZb6Cq+UukgNw94QUsNIwYNYn38B/l8/EwNe6mUAAAAASUVORK5CYII=)
PQ = 50√3
= 50 × 1.73
= 86.5 m
The height of a kite is 86.5 m.
Question 3.A circus artist is climbing from the ground along a rope stretched from the top of a vertical pole and tied at the ground. The height of pole is 10 m and the angle made by the rope with ground level has measure 30. Calculate the distance covered by the artist in climbing to the top of the pole.
Answer:Let PQ be the pole, whose height is 10 m and PR be the length of a rope stretched from the top of a vertical pole. The artist is moving from R to P.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANoAAACyCAYAAAAkutHsAAAAAXNSR0IArs4c6QAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAB1BSURBVHhe7V0JdFVFtt0ZX0aGhBAyEBJkCASZAogKIiIyNTihX0WhbVvbpdhiL9vZdmy/v1XUXv5vtwrazjIY2onugKgMgqAyySgg8xCChJCQ4SXh1y76xgcG84b77nv3vVMuVpDcW1V3n9pVp845dSr6uCqQIggIAn5FINqvtUvlgoAgoBEQoslAEAQsQECIZgHI0oQgIESTMSAIWICAEM0CkKUJQUCIJmNAELAAASGaBSBLE4KAEE3GgCBgAQJCNAtAliYEASGajAFBwAIEhGgWgCxNCAJCNBkDgoAFCAjRLABZmhAEhGgyBgQBCxAQolkAsjQRXAis3nEUM5cdwLGaBt0xnhOrV6fFBnVphSvPTvdLZ4VofoFVKg1mBFZuP4ppC/bigcvykJni0F0tOVKLZz/ZgcOVdfjdhVmmd1+IZjqkUmGwIxAbHYnsVAeuHJiOtJaxjd3dsKcS7y8/IEQLdgFK/+yDQIPSF49W1yui/dTndq0c+GZbuV8+QlY0v8AqlQY7AhERQKIjqrGbR47VYcmmMnTLTvJL14VofoFVKg1mBKIiI1Ba7sSt0zcgKf4EBfYdrkFKUgzuGZfrl64L0fwCq1QazAg0KAtjcnwUrh2coYwhcbqrins4Iz0erRNj/NJ1IZpfYJVKgxkB5n1zxETirE4tkdH6hNXR30WI5m+Epf6gQ4B+swblQquqPeFHs6II0axAWdoIKgQalMnRWd8AKzOaCtGCaghIZ6xAYHTvNuiTm6x9aVYVIZpVSEs7QYNAanIM+MfKIkSzEm1pK2wREKKFrehD/8NXrfwG8+d/itKSA0jPyMSIiy5C9x5nBuTDhWgBgV0a9TcC0195GVOnF2FTbQfUIR4xxzfh1Vnzcfet12LChAn+bv5n9QvRLIdcGvQ3AkXvz8ajL3+E/Rn/hRZtz0BUdAzqnU5s2LseD/31XWSmt8HQC0f4uxsn1S9EsxRuaczfCDhrazFjVhF2OgrRJrsAcFYDdTWIioxESl4/bC3ZjLffm4UhQ4chMsq64W9dS/5GWOoXBBQCO3dsw66DRxGfko2IhnrlK6s/gQt/NjgR064bth9ehoMH9iI9M8cyzIRolkEtDVmBgMMRp1TFaBX50VTUR4QiXx1iIuoRGWnt0Le2NSuQljbCGoGMzGy0TYpC9e4tSM7pq6KF69RKplYzRayGyCjU7l2NLoMT0Ca9naU4CdEshVsa8ycCFRUVWLp0KZIS4tFi33yUbW6ryRbtSISz6ijKNixA7xZ7cd3E+xEREenProjV0VJ0pTHLENi9ezfmzZuHzZs3o7B/f/Tu0wv/LP4SS1esQA1ikRhRjaGZdbj/zttQ2K+/Zf0yGpIVzXLIpUGzEfj666/xxRdf4MCBA8jJycGYMWOQl5eHyy8fj2mvvIQvF32BCy8aiWuu+zWyssxPvOPO9wjR3EFJnglKBKgqLly4EF999RXq6uowYMAAXHjhhWjVqpXub3b7HIwaM1alkovEiNFjA0Yy9kWIFpRDSDrVHAK7du3CggULsG7dOrRu3RrDhg1D7969ERv7U1Yr1lFRUYmqqir1s6K5Kv36eyGaX+GVys1GoL6+HmvWrNH7sdLSUuTm5uKCCy5Afn6+2U2ZWp8QzVQ4pTJ/IuCqKrKdc845B0OGDNErWrAXIVqwS0j6pxGgqlhcXIwtW7YgISEBQ4cOxcCBAxGtnNN2KPbopR2QlD76BQFGeHz77bfaqnjw4EFtVRwxYgQ6duyofGEqdZVNihDNJoIKx26Wl5dj8eLF2qpYq4KFqSoOHjzYFqriqfISooXjCLbBN+/cuROffvop1q9fr4k1fPhw9FeOaIfDujwfZsIkRDMTTanLZwSOq9RUq1at0iSjqtitWze9inXu3NnnugNZgRAtkOhL2ychUFlZic8++wwrVNgUHdCFhYV6JbODVbE5UQrRmkNIfm8JAq6xiozsOPfcc/WeLFId2AyFIkQLBSna+BuoKn7zzTc6lGrv3r3o1KmTtioyVjGUihAtlKRps28xrIo82sKIj7PPPhvnnXce0tLSbPYlzXdXiNY8RvKEHxCgA3r+/PnYuHEj2rRpow0e3JPFxFib2NQPn9ZklUI0q5CWdjQCNHIYsYo//vijdkAz4r5r164hjZAQLaTFG1wfd/ToUb0XW758uY7qMI61tGzpcr9tcHXZtN4I0UyDUir6JQR27NihfWObNm1CUlKSNtv369fPNrGKvkpXiOYrgvL+LyJgWBU///xzlJSU6BjFi1Rqbv4MpyJECydpW/ytxrGWZcuWaasiLYr0jaWkpFjck8A3J0QLvAxCsgfGsRYmy+EejFZFmu/tcqzFbKEI0cxGNMzro6rIYy0MpTp06JCOUeThTLvHKvoqViGarwjK+40IUFVkHg8SraamRhs7aPRo0aJF2KMkRAv7IWAOAIZV0VAVafAg0U5NlmNOa/arRYhmP5kFVY/pgOaxFloVmVeRjmdmpAq1WEVfQRei+YpgGL9/5MgRfQKasYosRqwiQ6qknIyAEE1GhFcI8AQ0YxXpgG7btq0m2VlnnYWoqCiv6gv1l4RooS5hk7+PVkUezKRV0YhVHDVqVNg5oD2FVYjmKWJh/DxjFbkXY657FsYqilXRvQEhRHMPp7B/ilZFmu43bNjQmCynV69eIXusxWyBC9HMRjTE6mPo1MqVK3VAMB3QZ5xxhrYq8iS0FPcREKK5j1XYPWkca2FeRZZwjlX0VfhCNF8RDNH3Gas4d+5cbNu2DcnJyY0kE6uidwIXonmHW8i+ZaiKtCoePnxYO55p8Ai3Yy1mC1iIZjaiNq6PyXKY455WRabg5iUS559/vo6+l+IbAkI03/ALmbe3b9+urYpMlsOEpSNHjkTfvn1tm4I72AQjRAs2iVjcH+O2FqqKPAHdvXt3faxFVEVzBSFEMxdPW9VmOKANqyJDqGi6D4UU3MEmCCFasEnEov64XuzHIGDux5hmwE53jlkElSnNCNFMgdE+lRixikz7xmMtVBFHjx6NDh062OcjbNhTIZoNheZtl6kq0qpIVZGE4wrGi9bFqugtou6/J0RzHytbP+kaq0hVkQSTWEXrRCpEsw7rgLRknICeN28eysrKtKpIknXp0iUg/QnXRoVoISx5OqCNYy0MneKdY4xX5P1jUqxFQIhmLd6WtUYHdHFxMX744Qedgptme94BLbGKlongpIaEaIHB3W+tMlaRIVS0KvJYC2MVebFfbm6u39qUiptHQIjWPEa2eYLJckgw4w5oZgceNGiQWBWDQIJCtCAQghldoFWRqiLzKqampuowKuZVDNWL/czAzMo6hGhWou2HthiryDugjWQ5BQUFOs89T0JL8Q0BquFm7WmFaL7JIqBv0wHNlG9MwU3C0djB2zPFAe2+WIqKirTz/rLLLmt8affu3Zg9ezaY4pyZlsePH+9zQlghmvsyCaonaVUkybZs2aKvQaLZnlmpIiMjg6qfwdoZp9Opo2TefPNNfSTIKMeOHcM777yj1e9JkyZh0aJFeOONN3DTTTehXbt2Xn+OEM1r6ALzoqtV0UjBTasi74KW4h4ClZWVesWidZZRMq73A3ACO3jwoF7F6G+kW4TJiVavXi1Ecw9e+z/FyA7OsMaxFsOqyNlXimcIcA/Lg63UCjh5GYV+x8TERL2isdCYxJwpTBbrS5EVzRf0LHzXsCp+//33SE9P16pinz59wvZiP1+gJ5EYJcPyr3/9S+/RjMI8Kbws0bDW8tgQ1XFXMnrTthDNG9QsfIexijR2MK8i/WRGshzJq+i7EIjtqcWVdL638FMNQjQz0TS5LiNWkeZ7zqo8nMmAYLnYz2SgXarj6XKqj64kJPl8NfML0fwnM59qNqyKVBVJLF7sxz2FrwL3qVNh8DJD1bgP5p6MezMSjm4U3vvmSxGi+YKeH96lP4whVDQ9l5aW6tTbJJnEKvoBbFUlieS6etF663A49L1vvI6K0TZ0BfTs2dOnDgjRfILP3JeNvIrLly/XFTOnIu8dk2Q55uLsWhuti64Ofq5iEydOxJw5c/DMM89oQ8mECROQlZXlUyeEaD7BZ97LtCrSArZ161btgKbpnnsyURXNw/jUmmhdvOGGG076Z1oZqUVMmTJFr2S0PvI5X4vvNfjagzB/n6oiHaeMVaRVMT8/X69kklfRmoFxukgakssMghlfIUSzRp5NtkJVkdmBGXnA2ZMhVIxEoPoiJbQQEKIFSJ68pYW+MaqKDPUZM2YMevfufVI4UIC6Js36AQEhmh9A/aUquXJxBWMuD8bUMQU3fWOSV9FiQVjcnBDNQsAZ3mPEKnJvYCTLofFDSmgjIESzSL50QDPlG4+18LgFk5fy/Jgca7FIAAFuRojmZwHQqki/GFVFrmh0PEsKbj+DHoTVC9H8KBRaFWm2Z6wi/TN0PvMENNO/SQkvBIRofpI3A1ONi/14uJBhVGeeeaapvhk/dV2q9QMCQjSTQWXcHFcwkoyqIlNv06ooyXJMBtpm1QnRTBQYIzu4F2NQMKMKGOFBo4ek4DYRZJtWJUQzSXC0KjJWkT8ZpEqS8QZNsSqaBLDNqxGi+ShAqoqMVeSxFq5oDEgdPny4OKB9xDXUXhei+SBR7sGoKjLSg4SjmsgMwRKr6AOoIfqqEM1LwTJGkQYPnoCmVXHo0KH6Yj/X1GVeVi2vhSACQjQPhWrkVeRKxuPuPXr00Bmp5AS0h0CG2eNCNA8EbhxroVXRNVmOpOD2AMQwfVSI5qbgjVhFqozMJcH9GE9ASxEE3EFAiNYMSoxVZGZgRt3zWEvnzp0xatQotG/f3h185RlBQCMgRPuFgcAU3NyLMdKDhZf60T8mqqKwx1MEhGinQYyxiszLzov9eKyFVkXGKsrFfp4OMXleVrQmxgBPQLum4GasIkkmKbiFML4gICuaC3quqiJXLqZ8Ewe0L8NL3jUQEKL9BwlaE3kCmtZFpuBmGJWk4BaimIVA2BONDmiegF64cCG4ovE4i1zsZ9bwknpkRVMIkFgMBmZQMFM/M8KDCXPkthYhiNkIhO2KxryKVBWpMjJWkWZ7qopmZqc1W1hSn30RCDuiUVVkCBX9Y1zRaLKn0UNiFe07iO3Q87AiGs+LcRXjxd9UFRlCJcly7DBM7d/HsCEaVUQ6oOmI5lU9VBULCwvlBLT9x7AtviDkiUYHNI0djFUsKSnRKbiZkSo7O9sWApJOhgYCIU00nhej2Z57Mt4zxlWMVkW52C80Bq+dviJkiUarIlVFpuDOyMjQpnve1iIX+9lpeIZOX0OOaFQVDasiL/mWO6BDZ7Da+UtCimg01xsX+zFWkSm4ebFfYmKinWUkfQ8BBEKGaIZV0bgDmmFUTJYjeRVDYJSGwCfYnmhM8+bqgO7atau2KsoJ6BAYnSH0CbYmmnGsxUjBzRz3dELLCegQGqEh8im2JRqtikYKbjqgaVWUFNwhMipN/Azu1XllVqCL7YhmqIqMumf6t27duukT0BKrGOihZH77x44dw86dO0FLsjdkYZjdjh07UFtbq0PuAllsRTSm4KZVcc2aNY0puOmElov9AjmE/Nf20qVLMXPmzCYboD/UOGnByZfB4kYhKY2M0TU1NSBh+TOQxTZEo+OZJKNVkaoizfY9e/Z0O1kOo0QYVOxwOJCZmXkS5pwx9+zZo2dNhmaJUzuQQ/Kntg8cOKBPWDDwm1dfkUxcmbgH5//TT0oC0X1TWVmp/z8uLk6fJ+QqRjlu3LhRZzFj2kAWPlNaWqpzc1rp9gl6ohFIHmmhqsjCFNxcxTyxKjIM69FHH9XAU3APPPAAxo4dq+vjbMf/50UVFAZzhNx9992WCiE4hnXw9YLyIhm49+YEaJCKEyLlSQKRWPz9bbfdpj+AJHz33Xcxbdq0RhkyaIFaD2X/+OOPY+3atdr1c//991tmOAtqou3fvx8ffPCBJhnVA4ZQXXrppR6piqxj0qRJuPnmmzWBeKf0HXfcgby8PE3al19+WQPPdtjGlVdeienTp2Py5Mle7QuCb7jav0dcxfiHBONNPQ8++CCWLFmCWbNmae3mxhtvxAsvvKD/neR7/vnn8Ze//EUbyJ577jksW7ZM+1OZ3SwhIQH//ve/9XjgcSk+Y0UJWqJ99913mDFjhl76qepRFTh06BAqKio8Ihp19ccee0wTlIVBxZzdWC+J9uGHH+Kqq65qvGrp6quvxuzZs3HDDTdooUgJPAIkGbUNqv3cp3/yySe45ZZbdAwrCydFTqL33nuv/l3Hjh01gUhMntbg5ErVMj8/X5Pzt7/9rSaeldcdBx3RuKrwcCZXGOrSBGfcuHEaqNdffx1z5szRM5i7+6iUlBRce+21WiAU0ttvv61nRxKOxKU60aFDh8bRROvlvn37UF1dLUQLPMcae0CZ0fhBGXKvxj0WycfxQnWRFmhmMKOVkhMzScYxY0QGcYvAf6eKuW7dOq06ZmVlWfaFQUU0nhd7//33sXjxYg0QZ6XRo0frjS+B7tOnj85Y1b9/f31o05NCUv3pT3/SdXMFIwHpi6uqqjopTwjbdbVgedKGPOs/BEgcajUkR3p6ur4PgftsaixcsTgp09BBo1daWpruCJ83imHepzuIf6wuQUM0zjI05VJlJJDMq9ivXz+92SVgdDzS0kgdnJEgnh55IbGeffZZTayJEyfqv5NwXBldfTT8e6B9LlYPAru0Z/jDqDbSgEXVnomVeByKK5uryZ/f5I3vzV9YBJxoVNFotudeibMSdWquYrQUUTWg6Z2FqwwPbDLEipvYXbt2eeSkNnwrnAFpWZw7d67W1blfo1phFPaH5A4mIflL+Haql/IgmbhHv/jiizXBioqKtMuG/0+Vkuok/50qIwuJZ0yagZZnQInGa5BoeGCaAYLCCA+uWlzROOBdVxaSjgQoKCjQxGR6gpycnGaj87lS0vLEGdDYixnZiLnKsS0Sl+RmoZmfm2QxhAQXDY09Gs39NMszNeDTTz+tO8mfVBd5GQmDyouLi/X4oYWSqyBJxrETyBIwotGkTqsib2vhSjVy5Ei996JliepdU4UzGv1nTBFHFZLqZXMBxDT/0rz7yCOPYMqUKZpI9Ks9/PDDmqSXXHKJNg3zSibu42iV4l6O/ZASPAgYKxINItxGUEa8q44BDJTZfffdpydmHo9666238NJLL+nziDSqcXwFeuK0nGh0OtKq+PHHH+uNK8HippaqItVDQ1VsSsSG+kjLIM24tDQ1RzTOcgw+pqOSwmCZOnUqGOnPQh8bV8snn3xS/7zrrru0lVNK8CFA+dBK/NBDD2nycGXjmKBsKU9OlBxPnDifeuopvbLRkMbxEuh9t6VEY0gNzfO0/BE0RngQIK46JFhzYBi/px7OWY0qoDsRIrRUvfjii6cdOddffz34R0pwI8BVjdoOf95+++36DwvJxj2a4WuldZraEsuXSxbjtddeU1uTyIB+nOlE+2Hr95j1/j+VSrgJ8QmJGDpkMMapFWv9xk2YqZb4DevXa32aqiKtijRO/NIqdio6VB9JTM5UVBuo8gV6oxtQCYZh4zR2GG4ZTr7G+OE44N9JutjYGCxZvAgvT3sVK5Z/heraOkQcb8CAgecEBDFTifbZp/Nxz2NTsaYyG9WOLPVhTsxY8jZef/NdtEtPUQCU62gMBonSl0HSeEIyIsSVkEGj3BRT9eRsJvnyAzJ2Atao4YIx/GSuE60OZFAnYp5T7ptpRUtQklyIiIKzMWPLfiy59WH88cbLdPiV1cU0om34bg3ueeIFrI0bjvguA5CsTasNyvpzPj78ehoKtnypvPK/xwi1ktHaR5IRIE+vqqUBgyuiQTQhmdVDxrr2jOgfGqbi4+ObtTBzPMXHx+HV6dPwtw9WoSL/ZiS3ztLvcULeU9IHT7zyHnKy0jF67ImQPKuKSUQ7js8WfIoV+xOQqlTFiIZqpTjXIEL9F5uQjLiC8ShbtxupKa20/4sqX3P7sdMBYMxehvrAmEWqn97WZxXQ0o77CBgypnGDGgxlTB9rc9oPiVnnrMG7M4twsNVwpKYpI4izCsfrGhAZEYmWWd2xa28PzCz6CCNG/QpR0THud8rHJ00hWq3yWXy3cQviU7IRoWYP1BmH8NQaXu+EIzkV5TEnDBIdcjuqX/90SM/b/nNF5GrITS9XNSGat0gG53skG/2sVA9pQHNnH85xUFqyHxu27kXSABXH2KDGmdKqdOHP+lrEtuuCneWHULJ/DzKycy37eFOIFqnPDSWoGYfOQa0i/1QY0qQ+ONJZruLUMvW5IjOIRuCpUtACSdVAiGbZmLGkIcqUvi86nTVP3EhFQKIlJcRh5aa9qKyvg+PUXCFqVeMKl+BwKi2oaQf2sZoG/G3eLizcWIbYmAi1EkZgbN82mDDoxEkBb4spRIuOiUVhz+5oKJqBuppqRMfEq+VaqY9KdUR0Aip3rsWZLWrx5yf+G61ap7oFmjsfRLJJ3kZ3kLLnM8bxGHd7r40kStU8fGQy/rF+LeIze6rxEaPGG+0BMWiIiIJzz0rkD2up1Mr0n1VbVlmHya9uRHRUBB68PA/JcdEoKa/F5Okbsf1gNe65OBdRkd4l+mmSaIcrnfhqyxEcOupE/X9W3gY1o7ROjMG4wjS9ap1aho0Yg2s+X443vpqOpIJxiGupjjHU1aJi2zK03PMx7nngZmRmtXcXM3lOEPAagdsm34pVd6iT1Ks/RItO5yI6XoViVR7Bke8/w8C2P+LXv/k9I45/Vv//Fu9CmRr7H9zVR61kJ37dJSMB037XHb/5+3r0yknCr9T496Y0SbTvdlXg+hfX44KCFHRMj9f1NjQcxyerSrFq+1E8eFmemilO7miaCuj880P3oOVTz2DmkldwoDxSLc+R6JVxHJP/MB7jr7jCm/7JO4KAxwgU9uuPFx6fgv95/iUsWLESZdXH0SopEhd3TsR9d96Jgh5n/qzOo1V1WLShDBf1SmkkmfFQ37wWGNq9Nd5bVoLhvVLhiPbc+d0k0aiXpiXH4o9jc9E7N6mxUz3aJ+GBGVsxVrG6b94J3dm1tM/pgGenPo0JK5ajZN9uOFQgZ6f8AhWk29ljsOQFQcAXBAYNGYr87gVYveobVBwpQ6uUVPToVaiDHZoq20qq8KNazfIzfn5PAxe/7tmJeG9pCcqP1SGtRazHXTvtHo0GjXLFcteSn5mI5PhorN9T2STR+Cz3awPPGeRxR+QFQcBsBNqktcWw4aPcqtZZx7wkQEx003swLj7U6v6TTMutOl0fOi3RyOIWilSuZfO+Y4rRTnRpJ7k0PEZaXghqBHLS4pDoiNJGj6bKvrJa0E5xOiI293FNq45KBa1xNuBFZebMbRuHaLUfS1CdmLuyFNcNzkBhx5+rjc01JL8XBIIZgbZKHeyTm4zitYfw6yGZmlBLNpVh24Eq9e8tMGdFCS4/qy1aJnhnqG/6LbWEckUjw1uqVW3bwSo8895W3HdNZzxyxRnBjJf0TRDwGoFbR7RX1sV1+MMbm/HQ+I4oU/uxNxbtxdMf7dAmf/rSTDXvK1UUscqyct15mYrNJ4wh8TFR+ODrg5ik2E6TpxRBINQQ6NQuHq/fUoAXi3fjqr+uRWpSNKqUZkdfWor6+/8p8/+9l+ShlRer2umNIYpsNHka5cZhWShefQj3vvM9Xrulh3LmqShpKYJAiCGQmxaPJ67uhP1qT0atjgtOjFrNdhyqwluL9uPHCqd5RHPWHwed1vxplJzUOEyd2AWXPr0aU/6xCVOv6+K1vhpispHPCTEEqB5mpZycyqKnCo7veY33tokmVzSqhk+q/Vh+5skq4rldW+HvN3bD/iMnLDBSBAFBwD0EmiRaZmsHrh3UrskaLh3Q1r2a5SlBQBBoRMA7W6UAKAgIAh4hIETzCC55WBDwDgEhmne4yVuCgEcICNE8gkseFgS8Q0CI5h1u8pYg4BECQjSP4JKHBQHvEBCieYebvCUIeISAEM0juORhQcA7BIRo3uEmbwkCHiHw//F+BY9m0BPtAAAAAElFTkSuQmCC)
The angle made by the rope with ground level has measure 30⁰.
∠PRQ = 30⁰
In ∆PQR,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
PR = 10 × 2
= 20 m
The distance covered by the artist in climbing to the top of the pole is 20m.
Question 4.A tree breaks due to a storm and the broken part bends such that the top of the tree touches the ground making an angle having measure 30 with the ground. The distance from the foot of the tree to the point where the top touches the ground is 30 m. Find the height of the tree.
Answer:Suppose AC is the tree broken at point B such that the broken part CB takes the position BD and touches the ground at D.
![](data:image/png;base64,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)
AD = 30 m
∠ADB = 30⁰
In ∆DAB,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
AB = 10√3
Now,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
BD = 20√3
So, height of the tree AC,
= AB + BC
= AB + BD
= 10√3 + 20√3
= 30√3
= 30 × 1.73
= 51.9 m
The height of the tree is 51.9 m.
Question 5.An electrician has to repair an electric fault on the pole of height 5 m. He needs to reach a point 2 m below the top of the pole to undertake the repair work. What should be the length of the ladder that he should use, which when inclined at an angle of measure 60 to the horizontal would enable him to reach the required position.
Answer:Let PR represent a polle oof length 5 m.
Q is a point 2 m below the top of the pole P to undertake the repair work.
![](data:image/png;base64,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)
PQ = 2 m
QR = 3 m
QS = Length of the ladder
∠QSR = 60⁰
In ∆QRS,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
QS = 2√3
= 2 × 1.73
= 3.46 m
The length of ladder is 3.46 m.
Question 6.As observed from a fixed point on the bank of a river, the angle of elevation of a temple on the opposite bank has measure 30. If the height of the temple is 20 m, find the width of the river.
Answer:Let PQ represent the temple and P is the top of the temple.
PQ = 20 m
R is a fixed point on the bank of a river from a temple on the opposite bank and QR is the width of the river.
![](data:image/png;base64,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)
∠PRQ = 30⁰
In ∆PQR,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
QR = 20√3
= 20 × 1.73
= 34.6 m
The width of the river is 34.6 m.
Question 7.As observed from the top of a hill 200 m high, the angles of depression of two vehicles situated on the same side of the hill are found to have measure 30 and 60 respectively. Find the distance between the two vehicles.
Answer:Let PQ be the hill with height = 200 m
R and S are two vehicles situated on the same side of the hill.
The angles of depression of vehicles R and S from P are 60⁰ and 30⁰ respectively, so
∠PRQ = ∠XPR = 60⁰
∠PSQ = ∠XPS = 30⁰
SR = Distance between the two vehicles
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)
In ∆PQR,
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFMAAAAtCAMAAADlRKeDAAAAAXNSR0IArs4c6QAAAI1QTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOgA6OjoAOjpmOjqQOmaQOma2OpDbZgAAZgBmZjoAZjqQZpDbZrbbZrb/kDoAkDo6kDpmkGY6kLbbkNv/tmYAtmY6tpA6tpBmttv/tv//25A627Zm27aQ29u229v/2////7Zm/9uQ/9u2/9vb//+2///bcvWoDAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAACCklEQVRIS92XW1vDIAyGYbqtzk3rYVareKJ1a7H8/59nErpSXB/XAlfmok8uxktCvgTG2L82Xd5yPn/BHHXO+frD9bxyF3zLVHr2CchssVeZ63khmVjCOskfGKtmEG3len5MWkUkgSE2KexhvQAmQjB1ZC721gtA1gmEaUj4tZ4/U2fXWPWYTJ1hmbrclz3PO06xhJzB2spAzNbzhEo8xgpIRlD4sZ5lSm7t1E71BahSC2C6JTfH25l+pFYbZ8Jsj1VS0KUbAlnvAGnu+juMQ5/6VUV1jGsCFVysDuMmBlw/Qd+K2TNTGU6FKFav4TjtuInClFhDMtJuoH3vEPDaJqzyDQ3tEFM5x4I3NxRckx7E1kXdNcL4Y/7aUa5WSWVyOvdexw24EE6dYNuCklqrqD3CTMMN1W9M2qOztgshnPG5w2KYKqQkGIFIoyETajBMCgpNo9yVO1p84ZKvTGgqTzi/ijJLGrr9Jxu+Rc63lB9V/9IRtvSZSXK2ZfqNREL3e5lMquJQCkYeVAL4du+Sydn2FwgTFanZMIOFjapGZp0Aro0zNHe825BJR0nM0ukVnzP4xZzaZ4NbHuWu0rmPIB14VyN6iUHuFQ3NIGurTJOSmEZWYYbvb9A8djUVCiTgPEJ86PodhgP9T8DeRKiYNg+HN40Q2TEY6rJX9z5Z/rGmSCLNxshxjcH9AEKtMNwCKrT5AAAAAElFTkSuQmCC)
![](data:image/png;base64,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)
In ∆PQS,
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGUAAAAtCAMAAACAqVX8AAAAAXNSR0IArs4c6QAAAJNQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOgA6OjoAOjo6OjpmOjqQOmaQOma2OpDbZgAAZgBmZjoAZjo6ZmY6ZpC2ZpDbZrbbZrb/kDoAkGY6kLyQkLbbkNv/tmYAtmY6tmZmtpA6tpBmttv/tv//25A625Bm27Zm27aQ2/+22////7Zm/9uQ/9u2//+2///b5S2pYgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAACKElEQVRYR+1X21LCMBDNFsF6xSoqLWrxQgXbpvn/r3N3k5RUCyOQzPDgPmSq09nTPXs2exDiPzYxoDKguPygF1Z3ACfTEGQ1ySmmjwcLIYpoKtQb3ASAURmiiAJSUceUX2XRi38YjVJhBblOT4/eo61FZcSawJII1nMwyioelU0yKik3N8p3sMiicYnZg6KYTw/PGBPUdj/1zRcp17bBiCvXIvAbTrNz4KkMUgqA7jqW9R4DDAPM5E9eapS0X656s1VwWsrH7UBqeW5rVjOAK75pd4tlDDg8oj7bzFwePQvJ153KRqU0d8ZuMPrtasudmdv7Vb9V7a2XOS2dwYK5GVMiSD+xSOd7WfB8HHAl8VfiLJWKh7WOL194PZiQs2vsBhFGKHsrZs1YHWNuc9xokCYBuMb8GkWfNnLevRR/2FN9KE1iUDAjb9c+lF4RtMidB9t9tZrgoNpaXBRedpaxvVdF2xdLFkJ1UHh/m+6vS8R/7cwYQ637YlBURllZv6yH/ZXMVuP1CQ95T93nTNp+aP8hW3l1m7/jbM4hSgWOzfgrgbSm7pCyGEbO8E+6IPARHRyp7VjCcZQ06mHMpeMoC7wGD6J5I3GOo9TLub4KwLPjKMOUoWXpOMrCKMe7YrpeD+X7EICvn45STmAYwCj9cpRkmb0z9ttRFiFcn+Mom1siKwgKXtXWUeICL4UM8cOi4yiXF7hHg4iMOn1EjtKD8Iyj9JDp6FJ8AyeIOb7GA1MSAAAAAElFTkSuQmCC)
![](data:image/png;base64,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)
QS = 200√3
Distance between the two vehicles situated on the same side of the hill = SR
= QS – QR
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHMAAAAqCAMAAAC3HJTrAAAAAXNSR0IArs4c6QAAAHhQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOjoAOjqQOmaQOma2OpDbZgAAZgA6ZjoAZjo6ZjpmZmZmZmaQZpDbZrb/kDoAkGY6kLbbkNv/tmYAttv/tv//25A627Zm27aQ29u22////7Zm/9uQ/9u2//+2///bewLruwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAB3klEQVRYR+1WyXKDMAzFaZPQLDTdQhqnNGWx//8Pq8XGmLAdYNKZooORjaQnPQtGQTBLsjgjCfokxObiaz3kXF/IEyURJKs00N9PQizLF40h8pAwdbxKi/jhq6p1QxYHgeYs8ghLHsIqF59BEXMdLaKiN3qf4ZoJcHKadVGvHLswT9rk20viMLlY3Ms1lY05tIncE0Yg0V5F4OA066PjJYKqaOdHqWGqaF+WXcvG88s2KWEitRh1lTrNGdIZJeRJDdM0BvBx2lJjNIt6PjOXjISr0youcPhzWINFB6aOOScVCbGtm1bzBzYAMzn2YEI22JOdmNQMLNewnduMO1wIg4n0WW59IgdgykpSmSivtpFgr4fA1PSQ50Tc3hTq3WceVjy8TQMqY1J3Ez1OK41tD9XY9TApVWwJhK7w3Fgnt5vfskywFbO7aVzriddgPxSNv4PCc79FhTslUPitmHZzmrEu3jmB3Dxpo08hNMLjh/mGmC2Mg+e79r5trHs+nBn43wxI+2vlr/F+UuYxgXKnqv4Mt3eqf4b1GBgynY9N2YDpfGzIIdP56JgU0Iw80wRvjNo9nU+RSM90PgUkxuyazqfChKm1ezqfArhvOh8Xc9h0PjbmgOl8XMh5Ou/g8xdDZCowvUqNmgAAAABJRU5ErkJggg==)
![](data:image/png;base64,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)
= 230.6
The distance between two vehicles is 230.36 m.
Question 8.A person standing on the bank of a river, observes that the angle subtended by a tree on the opposite bank has measure 60. When he retreats 20 m from the bank, he finds the angle to have measure 30. Find the height of the tree and the breadth of the river.
Answer:
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)
Let PM be the tree. OM represent the width of the river.
So, ∠PMO = 90⁰ and OA = 20 m
Let OM = Breadth of the river = x and
PM = Height of a tree = h
AM = OM + OA = x + 20
In ∆PMO,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
H = √3x …………(1)
In ∆PAM,
![](data:image/png;base64,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)
……………(2)
From (1) and (2) we get,
![](data:image/png;base64,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)
X + 20 = √3x × √3
X + 20 = 3x
3x – x = 20
2x = 20
X = 10
Now, h = √3x
= 1.73 × 10
= 17.3
The breadth of the river = OM = x = 10 m and
The height of the tree = PM = h = 17.3 m
Question 9.The shadow of a tower is 27 m, when the angle of elevation of the sun has measure 30. When the angle of elevation of the sun has measure 60, find the length of the shadow of the tower.
Answer:Let AB be the tower and CB its shadow when the angle of elevation of the sun is 30⁰.
![](data:image/png;base64,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)
∠ACB = 30⁰
∠B = 90⁰
CB = 27 m
DB is the shadow of the tower when the angle of elevation of the sun is 60⁰.
In ∆ACB,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
In ∆ADB,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
The length of the shadow of the tower is 9 m.
Question 10.From a point at the height 100 m above the sea level, the angles of depression of a ship in the sea is found to have measure 30. After some time the angle of depression of the ship has measure 45. Find the distance travelled by the ship during that time interval.
Answer:Let the ship travel from A to Bin given time. So, the distance travelled by ship is AB.
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)
Suppose, the observation point is at O.
OC = 100 m
The angle of depressions of A and B from O are 30⁰ and 45⁰ respectively.
∠OAC = ∠XOA = 30⁰
∠OBC = ∠XOB = 45⁰
In ∆OCB,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
BC = 100
In ∆OCA,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
100 + AB = 173
AB = 173 – 100
= 73 m
The distance travelled by ship during the given time is 73 m.
Question 11.From the top of a 300 m high light – house, the angles of depression of the top and foot of a tower have measure 30 and 60. Find the height of the tower.
Answer:Let AC be the lighthouse and ED be the tower.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKQAAADbCAYAAADjwTpVAAAAAXNSR0IArs4c6QAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAACy3SURBVHhe7Z0HgFXF1cf/2/vSm3QQkCKIICoaS0TsKIiigmKJGlBj1E8TjRolRiF2wUJsoCQxdqyIPZYgAQXpbelV2oLb2ze/wYvLuuXVfe1O8txl3y1zz/zv6edMYoUZcodLgTChQGKYzMOdhksBSwEXkC4QwooCLiDDajncybiAdDEQVhRwARlWy+FOxgWki4GwooALyLBajvCbTFFJua6bskyNMxN157DOSk+JD+okIxaQO/aWaO7qPTq8Y7aaZiWJf3+3Zq96tc1Qy4YpQSVaLF185oKd+sh8slITNPzIFurfKTuojx+xgCwoKdMD76xV5+ZpevI33XXf9NWavXKPpozpGVSCxdrFZ8zbrnOPbK68wjL9++stLiBrAkCbxql6YFRXXfPsUt38jxX6culuTR3bS51apMUaZoL2vMs352tOzh5NvKybNu4s0oOGAewtKFVWWvD4WPCuHDQy/Xzh3u0yNfaUNrrosYV6ZHRXdTsovR7uGju3+GTRLqMOJWtA5wbKa1OmJ2au1zvfbteFx7QMGhEiGpBQ5YfcYiUYPTuvqCxoRIrFC2PMzJy/Xeu3F+r6qcuUEBennG2F+sJIIheQNSDi8yW79OKXW3S/Ed2vfbPN6JPpGjGwRSziJ+DPvHhjntbtKNS9F3ZWa6MeMTobdej5zzYJUd61VXCkUcRyyDU/FOjWf63U4N6NdcPp7ZSSGK+/vJGjQ1qnq0/7rIAvUKxdEOB1Mi/4GX2bKs5wR8YhB2XoOfP3md/vcAFZFRBpyQm6fWhH/eqQhvarK359kA5umRZUhTtWQFlWXqFlm/I0dEDz/WDk2dOS4zWkXzMLyEuOa6XsIBg3EcshWzRI1unm7XUGHHJw7yaxgpmgPmd8fJz+fX1vZRjfY9XxJ8MEcvNLlZHyy+8CMamIBWQgHt69RvUUQEA3zKgeGokJcWpiAhHBGhEByKLCAv3vm6+1aMlyNW7YQMceO1Ct2nQIFk1i7rplpcXasnGdSktK1KhJM2U3+lny1Dcxwh6Qmzes0/W33K4PlxYpvmF7lRXuUYuH/6FxvxuhESMvqW96Rd39Vi5bogmPPKEZczcq37jOerbJ0HUXn6HzLhgZkmcNb0CWl+m2u+/TK4tS1PjosYqLj1diXIJy1s7TmHHPqku3bjq8/5EhIVw03HTtmtW6+uZ79NnOTsrocZYSElP1zbZVWnDfq6qIi9f5Iy6s98cMa0AuXbJIny3aoQb9r1GCSqXSfc7vxh37aefeDZo67SVlZTdQeUWcysvL9xOPurWEhAQlJibKkxq2eIBujq1rONfl2p4M3CWOy6Su4zmOedQ2X47hOYuLiz16Lu5Z8xwq9OSTj+vTTY3V9Ojhiiv50VyzTA3b9dHupDTdN+lFDR50kho2aV7X1AP6fd2rENDbeXexnNWrVZLU2HBGA4BKgFNZsVIbt9bHX32q1MTJSkxJPwCQ3t1l39GeAsfTa1cGrycvBSDnU9uxfL93715t2rTJY1ByTtVnA/jFRQX675wFyuj5e8VVlKii3LzwZlQYYKY2aKlt2w7SkiVLdfSxLiD3r3nbNm2UWLLbEMtU6iaZ+KAR4RY8ickq3L1Vfbt31JCzz1G54g8ApMNJyso8CyfCdUpL9y1IbYPrck2OrQvAfM9xnsyh8rG1XTc5OVmLFi3S2rVr1aFDB6WlpdXJKbl/VZADyNTkRKWmmvPN/wwMD3xsJExFoZKS6p9f1f8d61r1St/37HWo+rVP1evfva4mR41SfIIhXHyicjcuU9L6j3XlXXfomF8d78UV6/dQgMCnLvBazvTTsXW9ECkpKZo6dapGjhypI444wnLK2kZ1YATYO3fu0NZtW7Vq/bdKb3+0lJC874VPzlDBpm91aFquunfvUb8EM3cLa0DGG044/q5btOv6P+mrrx9TXIMOkhEpWXsW6q7fnaXjjj+x3gnmzQ291SE9uTaAZBQVFVkO6ak+yznoyXDMxYsX67///a85P0OdyuZr3exnldzp14pPTlN+ziy12v25xk34vTKyG3oypYAeE9aA5Em7dOuhN/71jD75+CMtWJqjJg2b6oTjRqln774BJURdF2MhFyxYYA879NBDDwDC9u3btW7dOjVq1EgdO3as61J+fd+gQQNlZmZasc2cUDfq0lEdo+2HH36wQPzuu++UnZ1tXugTjF/3O83+drZ2r1imvXn5OqlvN914501G8pzg1zx9PTnsAcmDNWjUREOHj9BQX5/Sz/N27dql22+/XVu3brXit5txN/3hD39QVlaWVqxYYX8HKBgbt9xyi0466SQ/71jz6V26dFG7du20cuVKa5XXNRyu+P333+uLL76wz9CzZ0+dfvrpxmhZoj15BfrDzTcacV1q9NMFGnvN79S85UF1XTZo30cEIIP29B5e+N1337Xc8T//+Y8949RTT9U777yjCy+8UBMmTFDfvn11xx136KOPPrL/7tGjh1q1auXh1b07DC6MQTN79mzl5eUZwyOpWg4JWBHncO+vvvrKzh8Rf+aZZ+qUU07Rxo0b7fO0bdtWp5x6mj755BMlpWYZPT14YUFPntQFpAdUOu2003TGGWfsP5KFRYf78ccftXTpUl133XX2u2OOOcYCBJEYLEByHzjchx9+qHnz5ulXv/qV8vPzD3gK5oCFP3/+fH399dfasmWLDjnkEPsMcPcSEyJ877337DMAUMQ3xhHiv6yye80D2gT6EBeQHlC0SZN9WUToX3//+98tRzr33HO1fv16u7gsKAPrFc6Um5vrwVV9PwQOPXHiRM2ZM0fHHXecVSOYU1VdEcDy8gwZMsQCF7UCrvn5559r4cKFOvroo62lzqhLD/V9tt6d6QLSC3oBvEGDBul///ufZs6cqc6dO1frkPfEzePFbX9xKCIbMDEPjKnWrVvv94/CFdEVMWC6d+9uxTM/HQMIbvnZZ59ZA+zss8+2L1G4gJEHdQHpBTIQlXwA3FNPPaVHH33UciDH+e0srCfGhhe3rfbQyy67TMOHD7fgGzVqlImsbLPiGUCmpqZaUXzCCSdYwwtx7LigOB7jCw7fqVMnf6cR8PNdQHpAUvQtxDBGDANdiw8GAYu/atUqHXzwwdqxY4fVy7CCgz0OP/xwK4pfeeUVNWvWTMuXL7eGCgYVIr1r166W8zEfBnol+i5qB5x98ODBwZ6iT9d3AekB2TAacO2gS2ZkZOj555/XsGHDLPeBC02ePNmC4tlnn7WLDViCPeDM5513nnU7YeBgRCGCHV0RIDocG72xsLDQegHglgC5cePGwZ6iT9d3AekB2RCNOKOnTZtmRd+VV16pCy64wJ6J3xEDA/GNXvbXv/7V6mXBHAANN86yZcssZ968ebMGDhxoAQngAF/lASBx/RAHxxMwYMCAYE7Pr2u7gPSQfIhBPlUHjucbbrjBw6v4f9jOnTutUYJBA4dGjZg7d67VHzFequqFvBw4wx1DBheWJ6l2/s/Utyu4gPSNbvV+FjorXPHjjz+2fkV0RCx+LG4Mrfvvv19TpkzRFVdcofbt21vdEeOK83CAo1+ef/759rxwHi4gw3l1fpob0RZ8h3BCjCi4HG4ffmc0b95cY8aM0cMPP6znnntOl156qeWUqBckUsA9cYjjAgr34QIyjFcIXRE3jsMVibbAFeGAVQcAvOmmm0wW+JPWJeVwQwweojZEaXCMh/twARmmK0RCB/FlojHp6aaDhAEUXNFJP6tu2ojv3//+99YL8M9//lMHHXSQjSZhxPTv3z9Mn/TAabmADMNlIhaOEYL1jKglewiweTJw/1x//fUiIeSNN96wlv9ZZ50VdMvfk7l5cowLSE+oVE/H4FhHV8SCxs9IitiRRx5pf/dm4Ctt0aKFWrZsacGMbzRShgvIMFgpLGHyFdEVcdGgK5544ok+J/uuNsVxn376qcid5DqRNFxAhni1sKARz99++63lhFUtaG+nh1McNw+GzLHHHmsjS5E0XECGaLVIyIArYrjgV8SpjQXtbxyctDIiMiQN9+rVK0RP5/ttXUD6Tjufz3S4In5FOBiZOUcddVStFrQnN8My//LLL9WwYUMbY6+PrCNP5uXNMS4gvaFWAI5FNKPfObpiILiiM61Zs2bZ1DJCnMHMWA8AGWq8hAvIYFK30rWdaEtVv2KgEjFIgfvmm2+s09zJAq+nRwvobVxABpScv7wY0RZKCbCgSaJFV/z1r39dbbTF16mQ4UM2D/FrDBmSLiJ1uIAM4srBFRHPOLqdaAt+RScGHahbA3hi1uRhUjMeycMFZBBWDwuaGLSjK8IVcVD7a0FXN9Xdu3fb5Anqfch1jERDpvJzuYAMMCDhirhyMF4QnVjQxJIDzRWdaTupZUR1KPaK9OECMkAr6HBFwOjoisHiis6UicigDhDnjmRDxuWQAQKhcxlKTp1oi+NXRFesLTPH3ykQiSHujSFDbTYlFtEwXA7pxyoSg3YsaEBJxR9ckWrEYA9UAmpqiMhw32gZLiB9XEkyc3DlIDLhiqR4EW2h3DTYY8+ePZY7whVx83jTki/Yc/P3+i4gvaQgfkVCfgCCaEt9ckWmyv0xZDCeSMQgCTeahgtIL1bT0RUBJNwJrogxESwLurqp0ReSaA8upEjJAveCxG4rFU+IhQWNrogFDWdyoi3B8CvWNh8iMsyBBlckT0SLIeNa2Z6g8KdjnJpmAOlY0PgVg2lB1zQ9pzlAv379bBJvNA5XZNewqk5/RTgSopraZyzoNmZniMrDqXtGt0OEVo4j00uHemj8hP6WEdAggLmQWoabJ5oMGZdD1sFacGwT9oMrArCaLGjyD++77z6tWbPGZns/88wzGj9+vHX7vP/++7a9Cq1O+P7OO+/0uYUJoKdJFOoCtdXUykTrcDlkpZV1LGjAyOI7XLGmkBzbcwC2l19+2V6FrhFvv/22rr76aj3yyCO2eP+cc86xHSVo9Ux5qtPc1BtAcQ9yHdFZcS1F83AB+dPqwhWd7hAOVyTaUpNfEcMC4NKn8a233rI9Iu+++27bIY3ECmpbjj9+3x46pJsByg0bNnjtxCYSQ09HXhYMGbKGonnEPCARh0Q9cHLj7IYrAqC6oi1s8YZu+eKLL6p3796WU1KcTyc06qlp6OSUrwIiAFxQUOA1lgA3qWXop9FqyLg6ZCWuiKHAouNCoW8ifkVPLGg4IBETIiV//vOf7RVpX0IbEzpMVG6T7GvLZNQGuCPF/tEWkanpzYxJDokFjcGCyIXLUZ0HV6xqQdfGzuB+iHaahjoDKxwA0Z2WvESn1TNc2Nmmw1MWCYjRG+G2tFGJ1BoZT5/XOS7mAIlf0cnixoWC0YE49La2Ba6FCKWU1Un9IooCcHCco/shxlEBqHdBbNNl19ORk5NjIzJY6dFuyMSkyIYrOhV/6IpwRSr+/IkFswHmQw89ZOtjaOrEZkb0aQSsOK8feOABXXzxxbZNHpWAnt4LfRNOy5xp0extKxVPQR+Ox8UEh6wcbUFXpPUx0RZ/M3MANGIb9w8i9t5777XpYAz8k5MmTdKrr75qfYfXXnutx+sPZ8SQgfPSbCqWRlQDEt2NRAgMFyIdcEX0PE85lSdAwDXEp+qAq918882eXOKAY5gnTnDUCWpkwrn9stcP58EJUQtI/Iq4crCgcUZjQQOccF9gOk/QWgVDJpAvjgdYCItDog6QWLaIPJzcjq6IBR0JBVDs8ErCL3HvaEwt8wTxUQVIOIsTg3YsaIwLby1oTwgX6GMwYJg71jmGTKR1LQsUPaICkI4Fja5InbLjV4wErugsJLou7iFeoFgzZKLK7YPjmIo//IFYvE60xV8LOlBvvCfXIWsINw9N6eGO0Zpa5gktIpZD4qtD30LMoSsST8aCjsSIBjUyRIwwZKI5tSxqAYmu6MSg0RWHDh1qfXbhbkFXtyBEczDCSOINlSHDfjbQLtjbKkcdILGgaQiPBY2/Dq6IBR2JXJHFcTbE5Hd6gfuTWuZ0WQPg/O6Ai9/xxzp/I6Ze3Xc44pE6oR4RI7Krs6CJtkSyvoWPFFcPhoy/W779+OOPdqtiGpay06sDRDgfagD6NRY83zubc/IC8DKjb2MMAkjAG8oR9oB0/IroihANrkiiaiRZ0NUtsLMFCIYMNTL+di0DSADusMMOsw2uAB3XJKEDg4k4O+4vstipXgSo/Pz3v/+tvLw8C0TmwjH0DHriiSdsYgdZ8PWpCoU1INetW2fF85IlS2y0hRh0Vb8inIHMGGqjq3IZMrQR7STbkvAQTsOpkQE87CkTiIEohhPCEdnjmz0QiaU/9thjNpZO6xUSPe655x6rHrDrF9yRrY0pvYDGMABASv4luu0HH3xgja36GmEJSN5cXDkQibeXUgByDKvqigCRjdUhLtV9o0ePttk1DPb4IxOHRYFbkPjgb+VfoBYFMU375WBEZOB0iF64I8/N3oejRo2yycOIcWhEt10kDGW1lF8ARKx8AMggQRl6Qvv6zjTyCJBFJeUqLauwk+W/ceaTnBSvpAR+C+xAXEyfPt0mpxKtAJwAsTrDhbcdMUO1H+exdzS5gxxLGth1111nKwYBI9WAZN94kg0e2Cc68GpwLrg+3Ayfoz+GTG3zhPOhFgAqAgVwPvTtpk2bWiCi/sCZASPABXj8ZF4XXXSRXnjhBcs5MRrrc9QKSIA49rml2pZbrOYNku28ysv3WXCXHt9Kx3UPnBgEeOiJgJHUfUQz6V38bcaMGVY3gttVHrfccostqmIgkiE4RMViZAHwSzIQ9YgsuIA3WeHBWAgMGeq1MchI5A3WgEsiujFwyAMFXNAEzsxLijqDvghHdYwc5sI6wD1rylTKLy7Tmm2F2pVXYjiuVGbw0KF5mto33bdVsr+jVkBys2Wb83XJsa002gCw8kgMIHfEVcFGkRALjkdZAKlX6EOAH04IUUlyrTycQqw333zT1rKQzUOP7WnTplmd0hE3XIcCK1+KrPwlcOXzeSFovwyXQg0Jpt8PQCKi2Yhz3Lhxys3NtVOhDogX14nvV51DXXOam7NXlz+1SCf2aKwG6YnKKyrT0k15euzSburV1v8elXWK7FQjmhtnJSnF/Az0cBIKABTpYjRtB3RkYPMd4o0UrD59+lhHOOKjaqIERAfElCKwixW1MpwbiCKrQD8vhgzJwhgyVbl9IO8FqOB80O/kk0+2XBLOjHTg5UdUE1BAT2c4akxdYOTYMqO6NclM0oSRXdQoYx98rjVS9C+v5+iFsb38xkmtgDTPZd5i6atlu5WcuE9fRGRnpCbomK4NlZ6S4DMdsaDxm8EVIdgFF1xg9T+4GmLDARQ6FrUrbJeG7oMorzwgIk5lPuiMZG9jAPF3xxnsFFn561rx+WHNiVi4To1M1Wfw57rVnctzwwXRDy+55BIbxYI21PygLtx6662WNhguGIYYV7wo0Louvy54iDf/MTbT/uEwrKRE/5lWHRwyzhgwcVq3vVDz1+61E8C4aWI45hGdGhhAek9Kp4MXFjQijJT/ylwRX1rlwb/pwcjbzFteeTEpvgesThEUgOPD8biDIDIGDuBnceCkoRjoaCTeosPV14aYvITQGq8DBh1gJPY/duxYu8ssgBw2bJhuvPFG6xbje/TMurhkQnyc1R/vfHmV5ZCFxs54f94OPTCyqwGq/9StFZDW228+I49tqWEDDjQofLm1oysiujBCsIpR7uGKVYHoXJ9FhINivFBI5ViLfA/XxIGLlb18+XLLbf/2t79ZkY+op2gfzov7h7oWxwDyZe7+nENqGfNDxw2mIePMEVDxIYsIkU0LFny5qDW8EDACrHAMF14UdOsck/rG8XX1usSQSTGcsG+HbLVoYLoFm3/nbC3Qc59tVP/O2fvFuK/0qlOH5ML5RnH1dHw/z+T1LV+qxKRk9enbT+06dLJvKtYyuiKuCLgchCKhAH2vJjBWBiX6D4YNoOQ8BuADkA8++KC9DlV+EJyBIYTrh+/4G07gut5+T5/Rm+N4Xl5AXioMtfqcAy8v6XlwQHIsoTMhWId78j1Roi2bN+jdN1/VwkULNOCIwzVo8Gk1PiIMKj0lXmf1a2p1SUbLhin6zd8Xa2tuUfABWVBcrr2FZQeAEl9kcoLxQ/6kVzKpMgOIBx+4X09Nn6vVP2YqId60p2v5mi456xijiMbrPz91YMBBy8JgnFTWFWtbZDg1ITAI6liLHM/iXnPNNfZTdeDyAIyhHvgcMdhwtQQqIuPpMzngx+fIx6GZw0ETTPjwn9Om6qFnXtPCPY1VFtdbl97+jC774r/6059uNdwyrdpbsf4HhLyNqE5LTjB+6SDrkOgLvdpkaMa87ZqTs8dODpZdWFKm845soaGVxPikSY/rnleXqKzrZWrasJkqzIznb1ulmx58Ssd3TtSZZ5+rwacMtpYebyYcrS7x4FCDWCrn4cqo7DPzdGFCdRwGA4YYOi0vYTAHlrKTRuZJdIVjPv/0I9056XVtaH6OMrv3MEwkQbl7dmrCOy8bNeph3WaMH2vVVhqlxqjdsttE0hbv1EGNUqwf8skPN2joEc0C4ousVWTj6pl8ZXdryDARZwDKylGaXdu36h/TP1Vxh5HKNmBUKR5/Kbt1D+3MHaK8khnqcnAna2RgYHjb6wbLD/8ZHJKwG7pgqLNSagIXz4ZhxctD+JKmVLh4AGcw54wRh8RBJBPl4veaBvNLNNzs2eenanVibzXtcLgqivaqoqxY6VkNVXbIOXp++mRddsk6tWrT/oDLdDROcGyKb1bkmueMs8xpoPG4XHdqYLZC8UiHxAlemyN8hQHJrqJ4pWQYK9Y8lNV0wW9pkTJamIadC8v17DOTlWq+93VRWGg+uE5YXKdvTjC5jq/X5gUCIIhqrHvmTLZNMAe0cTqyYezVNmycOz9PX89ZqMzDBpk1M3mQFfvSzirKipScnq2CtHZavmLFLwDZyQDynhEHB+1RPAJkXXdvbvS7xDgT7y4tUQqs8SdmGmdEQOGeH9S1QaIGnXyKklLSfAako/ewwIh6b7lsXc8QqO+ZJ9ycRGL0WLLA62O+3JdsJ6RIXbQBkKUlxdq6Y49m5e9VmtHxf5Z/ccYeMOlpRdvUzESU6nsEBJDtO3bS0T1aacWSWUo9dIgVBybircKiQlWs/0K/GXOOrvrt2Pp+tpDd75133rEgJCKDby9cR1ZmmuaMf1cFrfsrJS1VcYZLlsUlqWDdF+rfIUNdutZ/Y/2AADIuPlHj7rxVW66/VZ/MfV5q0UcVJYb1b/lKYwZ10MWjLw/XNQn4vNBxEc/4Qp0+PwG/SYAuOGz4CC1etkaPTZ+o3S2OUUJKpsq3LtDAxps1ftxfjUQLTMKEN9MNCCC5YZu27fTPpx/WE09P0UuvTlGTRg31m/8bqQsvGKH4xOBvt+bNQwfrWDwAxNwRmSRPeGLtBmsunlw3OTlF4+6+XYf1fl2PP/2CftiwVUOHnKHfXnmzWrUOjJHiyTwqHxMwQHLRhk2a66YbrjM+qXi1NW6a4edf4O18Ivp4EjvgkIQy/a2RqT9CxGvYucONTznRxrnHXjNWGZnZ9Xf7KncKKCC5dl5egdEdS5RfWHxAmC9kT1hPN3a2nSO1jMTbUCZyePvIcPT8wiIVFpfoR7N+UQVIb4kRDcfjgqIsgGgI9SfedMqNhucP5DMEnEMGcnKRci168uDmIYvGae8cKXMPt3m6gPRzRciUIWMGEU1OpqfhUD9vG7Wnu4D0c2nJQMIYwN/YpUsXP68W/qcTgcKTQJILddtsgeKMFSayQ6odg9p5p0+RkwNL5Ipk4Nri+i4g/cAAcWN0R3RGT5Jb/bhVWJyKNKDGmyIwEqMBJlWNFOORo8DGUXgYOI6qRUpuyXCizpuwJmmHnENiDWlv1aXiuYD0camdDTF566lqDGaNjI9TDPhpTkUiz0tNDgkkpNdR6wRnJOmFRGgGez3yN/yxSJDLL7/cckfKJF577TXbgaS65g0uIH1cNjLAKQkg8ZWs91gYlIDA9RhwPIrqOnXqZP9NNQAi3Bm8oGSgI8apr3c2u8ctxsvM+S4gA4QaEhgwZBiInlA3HwjQY3l8GepvnJooDDncXiSUVKYDGU9wUIDHcBrIOkkyNWV9uRzS42X4+UBqd+CQsWLIVCUR3O6qq66yNU1szUxtVE0vZeX2f56Q2gWkJ1SqdAxdNaiRQV8CkJEUkfHyUX9xuFPvDrejBAW/q1NWgvjFAncG3BEuCZ04D+MH0e20Cayp5bYLSC9XyWmWSi/zWDBkKpMHS5oKT1r6UThGQACLmkpKuswRHGAARnRK1BlcYYARiUL2E1yV3dQwiqobLiC9ACTF/tSGQ+RgF/t7Ma16OxQQAj7ENO4cAElNPZYzYKN+aPLkyVafpB6e5GS4JHrmzJkz7fckn2AY1bTtiQtID5fTce6ijPPmx2JEBjFL4wFqvDFWcHAjthlYz1deeaW1qlFj2AXXEcu4gnD5UBJM+XNtLbhdQHoISJJuEUNEJiq7Nzw8PaoOq6nZAU296M9U3YBmntDNBaQHUCG1DDcPCjpcIZYMGQ/IE9BDXEDWQU5ENPvIkFpGhMJNLQso/n5xMReQddAXxZ0ECnSgcK+RCS5U6ufqLiBroTP9FdnimM4ZbmqZC8j6oUAtd4Ez0rvcNWTqbylcDlkDrWn7wv4uGDLUyLijfijgArIaOhPeIjyIIUNPxVD1lawfCITXXVxAVrMe5O8RBqOUtSa/WngtY/TMxgVklbUkQQA3D1EGRHWspZaFGtouIKusAEm3hL/ouhs5xf6hhlHg7u8CshItqZFhHxmKk4hXu6P+KeACshLNKdgijQpDhp7g7qh/CriA/Inm5OkhrhHTbGPnjtBQwAWkoTtJpvgcnQ0xw71rWWigUj93dQFp6EyNDBEZDJlYKPavH2j5dpeYByR11QAyVor9fYNJ/Z0V84BkyzoMmaFDh7oRmfrDXY13imlAEpGhzsM1ZMIAiT9NIWYBiSFDnxmyv2n3EYs1MuEDw59nErOApEaGDgwYMiTfuiM8KBCTgKTYnxoZKuXqe0PM8Fj28J1FzAGSPjTsTEsZJ4aMG5EJL3DGHCDpoOAU+7sRmfACI7OJKUDS0gPuSDcFOry6qWUuIENKAadGhjxH15AJ6VK4fkhSy4hX08YDy9od4UmBmBDZdOMCjBgytB92DZnwBGPM6JAYMohresu4NTLhC8aYACSGDD5HGmxiyPDTHeFLgagX2VQP0pOQ8KBryIQvEJ2ZRTUgN23aZGtkMGQqb/AT/ssSuzOMWkDStQxRTbH/sGHD3NSyCMF41AJy8eLF+v7779WjRw/XkIkQMEatUeNsiEnXMspZXUMmchAZlRwSvTEnJ8caMk4P7MhZktieadQBkq5l1MiwSwAbQVa3wWNsL3l4P31UAZKuZSRPsC2Fa8iEN/Bqml1UARJDhoJ/ts7t06dPZK5IjM86agBZWFi4v0YmFjfEjBYcRw0gaTC6YcMGa1U7W+ZGyyLF0nNEBSA3b95sIzLsPehGZCIbvhEPSHYaZUNMGo0OHjzYTS2LbDxGfgmDUyPTrVs315CJcDBGfKSGhFuK/Snyd1PLogCN5hEiWmTPmTNH69evt4ZMhw4domNFYvwpIhaQGzduFB1vichQ7O+O6KBARAISQwarGkOGvZhr2p0+OpYotp4iIgHJBuK0X2bfZrfYP7oAG3GAxJBhHxkMGeqrnV3ro2tZYvdpIg6Q1MjQfhmr2o3IRB9wIwqQGDKklrVu3dot9o8+LNonihhAklpGsX9ubq5OPvlk15BxARlaClAf49TIHHrooaGdjHv3oFEgIjgkxf5wR2pj3A0xg4aFsLhwRAASn+O6det04oknujUyYQGb4E0i7AFJsT+WNcX+1Mi4I7opENaArFwjQ2pZo0aNons13KcLbyub+hg+FPv37t3bXa4YoEDYckji1KSW0XaZ+mq32D8G0BjOfshZs2YJRziGTPv27WNjNdynDE+RTftlLOuWLVu6hkyMgTTsRDapZRT705/njDPOcCMyLiBDSwGK/dkQk9Qy15AJ7VqE4u5hxSFpgcJ2waSWYci4qWWhgERo7xlWgJw7d66tkWGnBNeQCS0wQnX3sAEkXSfoeNu2bVsNHDgwVPRw7xtiCoQFINlHBjBiyJx++ulq0KBBiMni3j5UFAgLQBKNoUamZ8+eriETKiSEyX1DDkgiMjSKyszMdA2ZMAFFKKcRckDOnDlT8+bN07nnnusaMqFEQpjcO6SAZEOjDz/8ULt27dLs2bPtxkbu5kZhgowQTSNkgMSQefvtt237ZVqhkID7wAMP6JJLLvGopR6Vh5TDIurPPPPM/XtfFxcX691337XXJQ7erl27EJHWva0vFAgZIEmegCsSkTn//PNt8dbLL7+sRx991HakoJCrpsG5EyZMsN3OVqxYoffff18PP/ywsrKydNddd9kyWTjtW2+9pXvvvVd0RnNHZFAgJIBkdy24GKllcLGEhAS709bo0aP10ksvacqUKZZ61YGSWPeDDz6o0047TVdddZU97qKLLrLbgJDQS1LG66+/bvtE/vGPf9TTTz9tOa87IoMCIQHkjBkztGrVKgs4uBcgYys4ADpy5EjFx8dbUJIh3r9//wMoCUeEm8IdASZ9fZ566illZ2dbLkmEx9kPm2YCDz30kMrKyizo3RH+FKh3QGLIfPTRR2rTpo3VHQEKeh8DYLL71nnnnWfF9tSpU21TAOppnIEBtHTpUgtYMslJ4qUiceLEidq+fbvS09P3H5uWlmad7YDdBWT4g5EZVgvIotJyLduYpx/2lqisvELm/2qalaT+nbL9eioMmenTp4v+PKSW0UqP3RMqD0CZkZFh3UDok9OmTdMNN9xggcqgJNYR05TEXnHFFRo0aJBwH8Fh3Y2S/FqikJ9cLSA37CjShRMXql/HLLVtmqrSsgrNW7NXIwa21MhjWiolKd6niWPE0GS0V69e6tev337OWPViRUVFloMCWgwdOCC6JgPDhXi309wejkiEh1h4s2bNtHbt2v2Xg/NS+uCC1KflCslJ1QKy3BgHGakJ+uPZHdWjTYad2FLDMS+cuMByyiH9mnk9WdwwcEfEKBwNLuiI6uouBuccMGCA5s+fL3TOvn37Wn2Rn4AQYFMWi0gmQwhLnWu+8sor9m/ch/LZrl277ueuXk/aPaHeKVAtIOPMNPjsKSjdP6FDWmfo/KNa6sUvNuvUPk2UnOgdl3zvvfesJYx1fPDBB1t9sbbhGDmUv6IfAi6MIMTyxRdfbA0YEjHoogvHJH+Sa6Jv3nbbbbYzGrrq+PHj652o7g19p4BXRk13wy1nfr9D+UXlXgGSnRIABwYKXA0rui5A8kjonFjNZI5zPlYzSbs4zwEhjnEMG/RIRDOfSZMm6fnnn9fOnTt1//33W9XAHcGhgGNfJBjuFR8PC/N/eAXIRHNnPkaiezSwbAEeERkMGSIqFG7VJqorXxguiRhG7L755psC2OiLDHRKR6+sfA6uohtvvNGj+bkH+UaBEmNTfL1stx6fuV6pxp4ADucc0VznDmju2wUrneUVIFdvLbCiPCXJ87cBUYsxQ+tlfIr4BL0ZGDj4KtEfnRQ1b853jw0sBQDjfW+u1uyVe3TPiM7q1CJNKw0uRj++UEUl5brIGL3+jBoBCeTSk392Jheam70+e6vO7t9c6Sk1O5lTjY6Hngdn27Fjhw3fYWDAzfjpKXd0HsrRC7GgCQnCNRH57ggcBfBCpKaybsm2nqm2sXxTnj6Yv0MPXdxVh3XIsocebn6OO6+zVmzJt27CBD/Edw1WtqwP8qOFO7RtT7HKjIx+83/b1K5Zmi4wrp/axto1K5WzbIFKC/do+7Yt2mAs4GONvxAjwxO9sbprA0L0TyoS2aC9sqM8cMsSu1fau2e3li+ar1UrV2j1qmU67PABNRJj1bYCw5DihT1ReQw14rrY+K/jDbj9GdUCsll2sq4d3MaC8rPFO60fsqMB4y1DOtR6rxemPKtHXnhfi7dVKHnWImXsXaZBR/e01jFcDSPFl0GMmo01EdmEDV1A+kLF6s+ZO3uW/vLgk/pk6Y8qMo6PL1dO0LUjTtDVY66pVhLlF5epsKSiWjvCW89LdTOqFpCNMhJ1wxnetS+Z9uKLunHiDOV1GK6sbh1UbnTFnevnadaqGVq/NkdHHDnwF1EZT8mKZc1OXURpsJ7dERgKLFm8UL+97UF9V3Gkso3PNzUpRau3r9dNk19RQmKSrrr6t7+4UWpSwr7oXfmBX+G73pNfpuz0RMMlfZ+fV0ZNTbfZm7tTT059XXvbDVfDll1UUZqnBMO6G3U5RjnztuuJyc/ptkZNVFxSajNyvB1Y62QIIfLpF0mrFV+u4+19o/n4iopyPfPMM5q7t52aDhgkFf8olRUpq1kH5ep8PTL1WQ07Z4iatjjoADJ0a5WmJONpWbO9QI0y9+mQDPzT//pyi974v8OUluy7jh8QQC5ftkw/5BvF+KBmBowF2sfPDVsvLVRm6176esHH+tv4vyots6E1SnwZnIfIJxeSTCFvrXVf7hmt5/CCF+Tt1Qeffq3MtpcrrrzELNk+70dFab5SMpsoN6mdSWJZpmOrALJ760yd1Kuxbv3XSt0/sou6m4DJNytzjeW9Rted2tYvMHL/gACS+LJUblj5gS6duDijNxbsVcOMBPXs1VspaRk+A5LJoofi/sFadzmk768LdCwuKlDjhg20srhIaQcYIviZy5VYkmuy8Q80XJw73nRme6V+sEG3vrRSTYx6l1tQppvPaq/LT2zt+6R+OjMggOx0cBcd2i5bOZsWKK37yYoryzexRwPG8jgVrflKo0YM0h9u/ZPfk3UvEFgKFBbkadaTs1XS/igT8Egx7LFMFYnpKlj7lY5qXKJuh/So9oYZxu13y5D2GmsMX/TJ5MQ4wxkDk28aEEAmGmX4L3fcovW/u1PfzdupuOZm244yk+O44UuN6Jukq387JrCUdK8WEApcNGq0vlu0WlO+fFxlbY9TfFK6yn9Yqm4V83TvI3coLSOz1vtkmgScQI+AAJJJ9ejZSy///T5NevpFzZ4/XelpKTr54n666vLRymrg9gYP9MIF4npZWdl65G/j1GfqC3rzw/9YL0ifAZ109aV/Uc9D+wTiFl5fI2CA5M4dOnfTA+Pv8XoS7gmho0BqeqbGjBlrP+EwAgrIcHggdw6RTQEXkJG9flE3exeQUbekkf1ALiAje/2ibvYuIKNuSSP7gVxARvb6Rd3sXUBG3ZJG9gO5gIzs9Yu62buAjLoljewH+n8ew4rWl2KWEgAAAABJRU5ErkJggg==)
Height of lighthouse = AC = 300 m
Let ED = h
Let EB be the perpendicular from E to AC.
The angles of depression of the top E and bottom D of the tower ED measures 30⁰ and 60⁰ respectively from A.
∠AEB = 30⁰
∠ADC = 60⁰
In ∆ADC,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Now, In ∆AEB,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
AB = 100 m
Height of the tower ED = BC
= AC – AB
= 300 – 100
= 200 m
The height of the tower is 200m.
Question 12.As observed from a point 60 m above a lake, the angle of elevation of an advertising balloon has measure 30 and from the same point the angle of depression of the image of the balloon in the lake has measure 60. Calculate the height of the balloon above the lake.
Answer:Let BE be the surface of the lake.
![](data:image/png;base64,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)
A is a point 60 m above a lake.
F is the image of balloon C in the lake.
Horizontal line AD intersects CE in D.
∠CAD = 30⁰, ∠FAD = 60⁰, AB = 60 m
Let CE = h, BE = l
Then CD = h – 60, DF = h + 60
In ∆ADC,
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGgAAAAvCAMAAAA4n39HAAAAAXNSR0IArs4c6QAAAJBQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOjoAOjpmOjqQOmaQOma2OpC2OpDbZgAAZgBmZjoAZjo6ZjqQZpDbZrbbZrb/kDoAkDo6kDpmkGY6kLaQkLbbkNvbkNv/tmYAtmY6ttv/tv//25A627Zm27aQ29u229v/2////7Zm/9uQ/9u2/9vb//+2///bXd7oJQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAB/UlEQVRYR+1X20LCMAxdRMcQEMTbdKIFC7KL6///nUk3dhHXG+NFyRNsbU9yTpYmnnc2YoDDxbs7E9s7882JHkisAj9Gb0QEMF7XbmULGHwYe6kHSoLpjo4ToR9nYX10OlnzPoGS4LHwWrqUwFMjBjugtxXArJOBfD4s3zFyv/4rFbaJCK7XgnULVYVAzBGQ7xoRcdEmpBUdG7wuAKaxlEgK5QpEwaRByTyDvZUxihBuYm8bzHoGOpCqiMNjfrynbi+ZtUatiLqASPUyGZp5Y5UMaqDieIoIi8iBmlz/tVeuyzxQJEMaDGNvQ4sw4Ur+is0iClDQywez2pAAFrsUdzS/w9bWFJPuakmPsOTAhBQ725mB/8vAQcF0paIqvK0fmtN+36R86upf//t6o65/17Qn8gbH2sVHLBDP5v1jB4xZA5vfH1/L9X0lupg0r3VHZoyAGF5iYjPC+8qdQhMg8YK3PLtYellocaX/iNwEKB2jRIzok+2Em5kA8aohKjoYJ1MDfcnxYlUqk0WTxjBjCacCyiIgvvJbGUY+P6plUQF97iRVdXJvg1NRl2Iv7vE6ARLF3KOhUq2RwMGvWX8ksJspelc6EF/L5MYZgyA0qxUuyAZW8R5Hi40MQtC3mhUjx0mMw6iQKKMOHOe0U1k+d080O594D5XbDvEPrP4G5M0qk8soewMAAAAASUVORK5CYII=)
L = √3(h – 60)……….(1)
In ∆ADF,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
√3l = h + 60…………(2)
From equation (1) and (2),
√3[√3(h – 60)] = h + 60
3(h – 60) = h + 60
3h – 180 = h + 60
2h = 240
H = 120 m
The height of balloon above the lake is 120 m.
Question 13.Watching from a window 40 m high of a multi – storeyed building, the angle of elevation of the top of a tower is found to have measure 45. The angle of elevation of the top of the same tower from the bottom of the building is found to have measure 60. Find the height of the tower.
Answer:Let CD be the window, AB be the tower and D the point of observation.
![](data:image/png;base64,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)
CD = 40 m
Let the height of the tower = AB = h
Horizontal line DE intersects AB in E.
BE = CD = 40 m
AE = AB – BE = (h – 40)
∠AED = ∠ABC = 90⁰
Now, the angle of elevation of A from D is 45⁰ and the angle of elevation of A from C is 60⁰.
∠ADE = 45⁰, ∠ACB = 60⁰
In ∆AED and in ∆AEC,
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAF0AAAArCAMAAAAt1HQtAAAAAXNSR0IArs4c6QAAAHJQTFRFAAAAAAAAAAA6AABmADo6ADqQAGa2OgAAOjpmOjqQOmaQOpDbZgAAZgA6ZjoAZjo6ZmZmZpDbZrb/kDoAkGY6kNvbkNv/tmYAtmY6ttvbttv/tv//25A627Zm27aQ2////7Zm/7aQ/9uQ/9u2//+2///baOX7BAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABjElEQVRYR+WXb1PDIAzGl/qnWzedjrlqra7S8v2/oiGh9WZ3lHSgd8qLHi/gtycPIWSLxX8YNWSHhHE2AfSa15g9wKoSaQmg65zoRt0cW3X1KsFP07vNA9FpZQM7Gf3pGWDt2VKuWUFpZXebWxEdlpUpPeY3qyPRrTGWbr/Bg0L1xNvdHdgTpvM3eNBOnTs3S+iHi8YoNA3X1LsI9JGopv81R5f6fqL9fMgnp+pLgLG4YHo9cULnlE2dqt3Dd9Wmi/RQAQuNzsF3SdB7wrf3AIUkY4JT64cXvm/T1VY0SVbOJLHroqrT0W0e/SH6qEJJnB6tDXJmqInhE/6hIPps/d/pv+DMfO0BncpMuNlj3YPrx5nbk2wzyqZOtnxBOs9xiBoYryx6NltF/Q0/oR/9gx4hHKMs0ShuMagxKuNpd0SdI9jNI2juEY5IHRfN30SN3YQSR6fHmY81HR3JTQL6lzMRXR9OUueYkslOlTru+BnpblNmc5xv09AeX+6RqwSF/evVV4J0tfByvXLCJwc9HU1I3gy4AAAAAElFTkSuQmCC)
DE = h – 40 = BC ………..(1)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
H = (h – 40)√3
H = √3h – 40√3
H(√3 – 1) = 40√3
![](data:image/png;base64,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)
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![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
= 60 + 20(1.73)
= 60 + 34.6
= 94.6 m
The height of tower is 94.6 m.
Question 14.Two pillars of equal height stand on either side of a road, which is 100 m wide. The angles of elevation of the top of the pillars have measure 60 and 30 at a point on the road between the pillars. Find the position of the point from the nearest end of a pillars and the height of pillars.
Answer:Let AB and DE be two pillars of equal height.
AB = DE
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)
The angle of elevation of A and E from C are respectively 60⁰ and 30⁰ respectively.
∠ACB = 60⁰, ∠EDC = 30⁰ and BD = 100 m
Let BC = x
CD = BD – BC = 100 – BC = (100 – x)
In ∆ABC,
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEsAAAAqCAMAAADMOFYnAAAAAXNSR0IArs4c6QAAAJNQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOjoAOjqQOmY6OmaQOma2OpDbZgAAZgA6ZgBmZjpmZjqQZmYAZpCQZrbbZrb/kDoAkDo6kDpmkGYAkGY6kLbbkNv/tmYAtmY6tpA6ttv/tv/btv//25A627Zm27aQ29u229v/2////7Zm/9uQ/9u2/9vb//+2///bTBHFNwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABoklEQVRIS91Wa1fCMAxthsBQEPHFVLQqFmUP2v//60yasQ2Ono1mn7gfYJxD75Kbm6RKnRtcMkoxJ5cAIZrRj1BkEL3RWTsfI+MH4Gcw9EN8TYddQix27qMMg12s90kylyAuM1Zm8LWPa/cypOcwuGSp8nhZiT/6DOOhU/llWirl9XKaCxEE451ASYq1tzcURgaYJHO5xIsXgsw7gK31lyc4bEYLP59HLgyGCTV4s5VwT53Vs3MADIy+BmvuoYvH5uvtXbhxj9PIBMY95tJUk80EYNg51/9Udc9YUx29qiIR2I7ZychKU56GXCOCqWqqg12n1G5LQbyXKhWraXCbFis/Ee3CtwBZZnrgDV35t13Gn63PqXbEd9yeY6NDDpslp1lrar2zg3Y4rQjU4s0G8twVTskRD+Ho8I7AlicWP0lCgZtuU64U1LfglRAKAxMOpVjFAKKtyXOoL+CCOiOgXUYpTnZB2Rvew7LT0u0DdG2q54uQMY+vZkKK+rhpHx5d32Vv7/tyJk4E0b2rEbLT2MWSCVVz4a03wrhAMO66ain73y+S3SEDWh6GdwAAAABJRU5ErkJggg==)
… …. (1)
In ∆EDC,
![](data:image/png;base64,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)
(AB = DE)
100 – x = √3AB
![](data:image/png;base64,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)
100√3 – AB = 3AB
4AB = 100√3
AB = 25√3
= 25 × 1.73
= 43.25 m
The height of the pillar is 43.25 m.
From equation(1),
![](data:image/png;base64,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)
![](data:image/png;base64,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)
= 25
The distance of the point from the nearest end of the pillars is 25 m and the height of each pillar is 43.25 m.
Question 15.The angles of elevation of the top of a tower from two points at distance a and b metres from the base and in the same straight line with it are complementary. Prove that the height of the tower is
metres.
Answer:AB is a tower. D and Care two points on the same side of a tower, BD = a and BC = b.
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yMDMPqkTgYaqyed1dtUsIGlJp8LkwGqwoFVS3kiJ8JBy6mHhMUU4/DVkLJgVtd94qLi80eyhNQSkrUYjJ4vKqgCkCOAAhWDyIiOztbunTpYlg9rqAJ5hHKATS1ylfsPRSAUlLCLan+VI+Cyk+Zwubhw+G2DGL1SGfnlsFQZfW8u+e5h1JSws/Bd/i4gsqhoHJycoyphLlHIb8JVq8ujlB22ESfj2HyQUqQq4WGIlKCPaAWdyWgoPIhT66bwdRDO+3evduYeieddJL5MxxMPbt7duiRDSgiJRRQ7oLJrk1BVYNcuRiNc/Uw+TD1Tj/9dHMxWriYenbXvEkJAKWkRHAARa0Kqipku2fPHuNv4rAVIg2IhOCnPg9bCXQKeJISnHMBba4aKlBpOntPQeUhJyYg9DimHpEROEMx9ThXLxwL/fn4448r91Bq8tXNKCqo/idnTDyICNIyWMnPPfdck5ZR34etBDoNbFKCPtkaSqPNA5Wmf+9FPajQSKRlcHUnph70+LBhw8J6z2HT5pASnHehJp9/oKjt01ELKvuwFVZyHLhdu3Y1FDkO3HAu3rS5mnx1P5pRCao1a9aYfRMmH0co27F6ycnJdT8CLn7RE1C2hoK11FK3EogqUHEHLqweqRkVFRWVrF44xOr5mhaepASAIn1DAeVLasH5fVSACgcu9DiAsmP1hg8fbky+SChoKJvlA1CaAl+/oxrxoNqwYYMhIjD5OPObWL1QPGwl0GlgA4oFg3R93UMFKkn33otYUKGRiNMjcRBTDxKCSPJIiiSoyuRTx6574Ai0pogDFTFumHqkZbCH8kzLCFRIofge7KUdHIvJR3Cs7qFCY6QiBlTl5eWGzSMDl0NXcHSOHj1a+vfvL+HO6nlPFdsPhcnHoqGkRGiAyW5FRIAKBy5gIsQoLi7O3JYxZMiQsMjA9Xc6oKEgJQCUzfKpyeevFIP7fFiDymb1iBwAWN27dzdgYvWOxOJJStBHIiWaNGkSiV0N6z6FLajWrVsnc+bMEdIz2EtwBy5pGYmJiWE9INU1HpNvxowZRkPB8mHyKaBCc6jDDlQctsLE4pB/WD0OWiELNxzTMpxOCU+TD0ChoSKVlOAq1n/84x/mfuMxY8YYxtYu06ZNM5EwmLu33XabWUBZbF588UXBdXLjjTeazILaFrYQtbkXLGxAhekDRQ6gMPXYT3CuXqQ4cKubCDag6DsmH36oSAUUmdXXXHONOStx6NCh8sQTT8iBAwfktNNOkw8++MCA7frrrzfX+9xxxx0yefJkY62Q/4bZ/9xzz8mDDz5YKUrmDASWvwBhW8F7gZawAJV92AppGThwYfWIJo80Vs97EAsKCuSNN94wiwn3V0UyoOj79OnTJT8/Xx555BFDOHGZw5QpU8yR2a+99pr85je/MSk5+Bz5O5kFzAfe4fI8z3MW+R31ocn8BRVakjNJyFoIpIQ0qDjplShyBMTKwZ6JFSka8oIAFBMJfxu+NyZZpGooe+Jy1RDamL5S+Pv27duFw0rxOfbu3dv8O+NPIPTq1avl0ksvlc2bNxtQXXvttZUYIIKGw02ZMwkJCWar4KRw7ghbjC1bthhQB1JCElSoX4BkZ+DC6mEChNPJRYEMhv0O/QdQnI/Rs2dPw2rOmjVLWrZsKWeddVZl1Uw0fHKEXTFxMJU4Oo13Qv103KrkQz9mz54tmG1JSUkyd+5cAyYWV/6NPlJszcO/UbBcvAvPED1DWBqycAIQ3omPjzcB1wDWKRC9vx1yoGJSACbYPYRy3nnnmZNf8UM9//zz5gaNm2++2XSewo3ubFT3799vgOe5sa3NxK6vd9FQr776qgEU+0XMHKLoAczbb79tVmlWXwp9Zo9BNMWtt94qt99+u1m1X3755bAE1amnnir/+c9/TJ85woA5AJAAWKDkAUCxf3yNqdPnfNUTMqBiNYIyZoVAtWPmcdgKNvNHH31k7OzLLrvMsDxMIP4f9ufuu+82qxDPskllYnGuRDgWbHlbQ6GdLrnkEtN/zD9cBpg4bNi5NI7VFyaQzfqdd95pJh+m8ocffmjeCccCeB544AFzpgYEDeYfoVgcB8D+mQWUwlaAHyeXjdvPOiEeABXPBaqhbJnXO6i4ZZB9A+YNdiy+F3ww9mrMhPrb3/5m/u2qq64yHcaOJvKc62lWrFhhJhpAZHPJKg8gPc/kA6gwSzbYIDy2bt1q0uZD5ew+APXKK68YDdWtWzfTR9wEtokDiDgi7dlnn5WsrCzDfFK4kZGV/aabbpLXX3/dFUq5vgDJonDXXXcZhpdy5ZVXmn0Ue8l27doZgGGJEDmDWcglEKFY6hVU7JumTp1qtBP7BYCDQFH7NqgAHewOMXwUVhOe5YBLqFT+DqAo2OTUB+PjyQwyAFdccYU888wzZhJefPHFJtuXv4dCwbRjMYAeBlDjxo37GaBoI33id7CeaG7kYRM2yIdib/BDoU+BtAGQ8DN27FgzfpyvyLhRMPknTZokN9xwgyxfvlyuu+66kI2cqRdQYcbYdyJhurHq4sTlKGJWZlZitAirE5oLZx+CtEFAOgerNo5CTIZKtWvts6BBvdU3dd9zzz3GPHz//feNOXHvvfcGMu6uv2ObfAAKk89bQ9kfxCyhr8gFfw2+ml//+tdmr4mmZsF46qmnKoHnekProEIuF3/yySeN+YeFglayx7dv376m3yzAAI0FNFRLnYKKCQS7w2YU7cHKC1AQGKssqzEaigm2cuVKAyoICTzl999/v7GzmVw4f3neJits4aLFAFRVK/b48eMNkF944QXDmIVC8dZQ1QHKbivyYUFAbmhzQrRYsenb7373O0M/YyKjrd2ILKgPGTF2mO9VFcz9UL6RsnJxrwvBAQTsYO5DQuNgshFqQzQ5phvaCY3F/obNJ9ESmIZoMMgItBLa6ptvvjFAw/lHHTyLHW4XqGhMIlYzVjVA2LZtW+N9Z7AwF6mPBEZuvKjP4gmomjSUZxtZMJARgMH8hf1DA9uUMv2ETg93M7A+x8WNbwddU0EIYHJh0qFJUOmcD9GmTRujdZj4niYOlDn7Bt5hPwWTdfnll0u/fv2MXY3JB/M3ceJE8z7kBjQyICElglUc1oiNO7/HNqdOzD0AjInE7+qTJbP9UL5MvqoGGLMIEKJ1kS10ul0gMzAJtdROArYfzN9IjKBrKgCBvwntBF3OCoqph/+BxjI5qqMuYb1YbfGwAyqo5b/85S8GUGT1Xn311YZORrtBOEyYMMGACnPo8ccfNyDie3YhEJNwl3feecds8AEfdjl+n7q+bAA/FH4kHJuAA1KCPtosn6/pQJ8xgdDAsJiYhJEame9LFm7/HiuAPVxCfKxYQVKSaP0ZSAlYU1WUH5LpH30gb30wS3bu3iddO7aVKy8eI/0GDDSmG5rG04GLHwlzjclTkx+AScNzaBW0EDFvmIGYfYSdACKCLSkADz8VKz4gRntVFXXB5LUBxXuYhoDTe08WiABreufHDevkn69OkUXL11l+pRQZMbi/lJeVyryshQEByvNbLCIsOpiRmqRY+5Eze/S4WPnskxnyz9ffk2+XrpT8x56Wm6/Ok1NGnu7XBwICFQzb008/LX9+ea7ktRgmkpIhX6zcIp/e9KiMHtxBCgoKpdhaQdFMsFXsfzDFWFUpNalVAAegMGV27NhR2RnMOn6qKnyjpuKptXiOfRfe+2CWNWsslmrCH2XRgc5SkXmaxORalwW88KW0Klgsl140WsZddrlpB4uMP2YGqyk/AAkfnaf5HMz+hFvdniacr0gJ5Inz/K0pb8qfnp8huS1GSMLgsfLpvs0y/9a/y+O3ZFuBB+OYuY7EEBCo5n81V+5/abaUDZgg6Smplou7VKRtDysQsYs8//a9ctV5J8ll4682IKBDNpictAjwcSkAZhkb8XAsZaXFcs+fHpbF5cdJWv9TJPZQkTUelkHRrp/8+Pn/SUJcjNlTol39LciHVRUTFzZVQVW1BP2JigBQK5culof++aEU9r5RUhu3lJhDxZKccYQUZnaTe578uww8qrf07OvM2RwQqObNXyD5DbpI44bWkcIlhx2PUnJAUjI7SFHrQZK9e69kWU5czDJ/OmeLByBi+mGesReiBFKPvxPWjecZoK2bN0rWqu2SPOASiS0rtBpPtHOZxCekSErXEfLBLKtPMQ9LXEJSQHk7rKyYfRAeuCfYgzoJGHWjf6Feh62V2G8S1oRTnXlU0/yJj4+TxQvmyZ7Y1tIovbVIcb6YmPbyMmnQpKXsjO8q8xctCS6ocvMOSGz8T07XSjBYf4lNbCg7szfKuvXrLEfsIb9MG0/wsBqzAYd8CKeSaIFqg9X3g2WWvyzWa82yTNv4pBTZk1MgG75fL0kNUgMCFROEyYOzFDcB5IeT2LZwkmNt2sqiY0fVwJDa8qquzrjYGNm8ZZvExLc1Bp5nkkhFRbkkNkiTvHxrcXRYAtJU/fv0kJIPP5Zy6+txcVauioXomLhEyxQpkITctXLH5D9I1x59aq1dbGA57EtIPMZkP5C7XxasuVVW5eyUJq27S0VpAcuNJaxkyd+0RC4d2k9uueVWibEGvzYamG+x8IRK/GJIDMD/GoHmdrrtQI6Ls76U8fe/J6XWvj8hLsma01ZyY2yilBFgu2u59OtxjePuBQSq4SNGyrkffS7vL35b0nqOlITkRlKcu1sKV02T2381WEaeea7jBkTkgxYx84erLpIbHpsmuTHnSaNmR8ghi/XLXT1LeidtsNI1/iSdLJeAltCRQLs2rWXW10vl+fmvS2qvcySxYRMpKciR/NXT5fKhHeW4wSc6bmxAoMps3lKefOhuaf7oEzJ1wTOSV1QhbZvEyiWj+8htt/ze8ccj+cFLLh1n6PO//muqdY57maQkxMqZXRvJHy0N1bPX4QxWLaEjgfjEJHnwvjuk8eS/yptznpdd+eXSPC1OfmsB6q6Jt0jD1MNB205KQKCi4vYdOskzTz0uv1+zSgoL8iW9aXPp2KW7k29GzTPjLr9CRljUffb2zZJgDdoRnbpJaprzwQl1QeHygIHEYYozOtxL08zm8ugjD8tVaywflWXCpzZOly7dDwcr+FMCBhUfiYtPkCN79/fne1H3bOu27YWfSCswu8Ri4i+DLOEGShIpIyHusOuRtbMkHIFqb74VUmT9l5xg+UeSDx/KocW3BErKyqWwuNza7MInRY78CBcjsZSYTIJ7CUd76623TKSLndvmWzqR+0SNoNqdVyL/XrhLZi7bK2kp8cIkufjEVnL2gMzIlYhLPcstLJPxz66yqO4KaZYGi1QhyPPO0R1lcLfGEuunSeFSs1yphjMzCORFQxGYTCoOviCl9Q+Lt1pQ7S8olQmvrpPGDeLkpWt7SXrDeJm7ep9c/9JaSUmMlVN6Z7gyQJFaScmhCtm2v1jutkA06pjDZ0bMXrlPJryyViZf3FWGh7H8CJAmZ4uDeUjfIaQMJ2tt3AOhNg9WbTkg05fskeJSDuMUKSopl1P7ZMiwXr7nfbWg+nJNjmTnFMvff9vXAIpycs8MmTSmo+yzAKelZgmwtU2yopzjrZAku7AQAbBXPt8hJ3RvIkkWIxiOhROvcDgTzEzBFCRcKtgBynUpq6/X5siLc7bLAxd1NuO0fV+x3DXle3n0km4y5MgmNTalWlB9v6NQWjRJlIyGh89as8vYwS2tFakuuxfe3/KWFWD6ZNkewTxs3jg8L1PgWGZSV958802TFcCeCmcrh1AS5REJJd5aELu2aiAXDGpR2Z253+2XqdZ2KGBQFZZYHmkr1IY9thXF8bMSxtuBeh9vVr0GiVZwbeBHddd7H0jDgaRAYxF/SBY3h894nhdS742sZQOY8iWW6bfvQKlF0Fmn1lpZBmWWSX9G/6Y+a65WU6X+j5jwBhR7rTxrlT2iWYrPyvWBX0qAQcI+T3DEu4auBMmujtR7wJA6mQQbdxXJza+ttf4eK8z7NdsKJK2B74Gr9omBnRvLB4t3y4bsIunc4icA3f7GesNovWiRF1p8S8BzT8XT0yzz4ehOadLEy6z2XZM+UZcSKLW0Uidr3j81/kijqYosy+1Oa0/12Eeb5M0b+1hZwdU7hKsF1aCujeW4LmmGrZp0XkdpnZ4k78zPlqz1ufLqdbVzjtWlcOrrW+ylDhw8JFv3HpSt1iaXjegMi01i9XtiXDeJ9zYB6quh+t1qJRBn7XMaJFnZEpbWAlijjm4mk6dvkmLLtZRopYtUV6oFFWP+5ws7yzMzt8oTMzZLskWjowbfsFDat30jHQofEsDtMNRiieau3i8LN+RZ9ni52Uf96/re0j4zWeUX4hJgUYy1QACg7LJoY550ap5isbo1hy3VaCACoglntpcJIS6AUGwekSdPjtdYyFAcGydtsqa+rNtRYJl8640y2WvthXdaLqbJF3fzeSCM712XkxboMyqBCJPAOZap16NNQ8ktsnIFrf9KLTPjqA6p0rLJL5NzvbuuoIqwyaDdcUcCGY0S5NgugWUUKKjcGQOtRSVQKQEFlU4GlYDLElBQuSBQTu0ht4jgUicXkbnwSa0ihCWgoHJhcEh9ePfdd82R1goqFwQa5lUoqFwYQLJdyYAlFo6jqck38j4V14XPaBVhIgEFlQsDBai4b4trfYjg5k/Omxs5cqQLtWsV4SYBBZULI2Yn540ZM8aAiiOdSeLjArtISYVwQUxRU4WCyoWh5sIGrsPB7KNwshAn8HBjI3dtaYkuCSiogjTe9iUCQapeqw1hCSioXBgc0sg5A487d9PT081lbNxaEq737rogkqiuQkHlwvCzp+JMc64MXbhwoSEpOAMvkjJhXRBT1FShoHJhqLnKZtKkSSa1nGO7YP0gK7REpwQUVC6MOxrJJik6dOjgQo1aRThLQEEVzqOnbQ9JCSioQnJYtFHhLAEFVTiPnrY9JCWgoArJYdFGhbME/h90KTd77RBUHAAAAABJRU5ErkJggg==)
∠ADB and ∠ACB are the complementary angles.
If ∠ADB = x, then ∠ACB = 90 – x
In ∆ADB,
![](data:image/png;base64,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)
………… (1)
In ∆ABC,
![](data:image/png;base64,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)
…………....(2)
Multiplying (1) and (2),
![](data:image/png;base64,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)
![](data:image/png;base64,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)
(AB)2 = ab
AB = √ab
Height of tower = AB = √ab
Hence proved.
Question 16.A man on the top of a vertical tower observes a car moving at a uniform speed coming directly towards it. If it takes 12 minutes for the angle of depression to change its measure from 30 to 45, how soon after this, will the car reach the tower?
Answer:Let AB be the tower with height of tower AB = h
![](data:image/png;base64,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)
At C the angle of depression of car measures 30 and 12 minutes later it reaches D where angle of depression is 45.
Let CD = x, D = y
Here, AB = h, ∠ACB = ∠XAC = 30⁰
∠ADB = ∠XAD = 45⁰
In ∆ACB,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
x + y = √3h ……(1)
In ∆ABD,
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADMAAAAuCAMAAACyN9FdAAAAAXNSR0IArs4c6QAAAG9QTFRFAAAAAAAAAAA6AABmADo6ADqQAGa2OgAAOjpmOmaQOma2OpCQOpDbZgAAZjoAZjo6ZjpmZpDbZrb/kDoAkDo6kGYAkGY6kNvbkNv/tmYAtmY6ttv/tv//25A627aQ2////7Zm/9uQ/9u2//+2///bRSFjMQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAA2UlEQVRIS92VWw+CMAyFWxUR7zpvE5Gi/f+/0Y6oMSQkO8ZEtA887aztt9NC1LUouHeAa5JOa/ZH5inUk/AoV481Jbwmqj/xUXOr0v/R4AyEzXBVyhi4eMQtJ88L1OWXOfdPWN4qywtUYxm+pfH8iHbnR9X2vIdrXlGaBtmm5mO1NfNgQ06kO/MqD1aYE37+tDrmpLQ5RXipS0rbiYjk7pZiCBELK1Q32ESrG5KE+pAwW3poW9vl19lkCS4OIg/+sUIT8sauEQx0oIyCJnXjLZjGNJyBb/P6jjcwjw4XtCJjiAAAAABJRU5ErkJggg==)
H = y ………(2)
From equation 1 and 2,
x + y = √3y
x = (√3 – 1)y
The distance covered by car in 12 minutes is CD = x
So, time taken to cover distance x is 12 minutes.
So, y = Time taken to cover distance DB
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFAAAAAmCAMAAABktOxDAAAAAXNSR0IArs4c6QAAAHtQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOgA6OmY6OmaQOma2OpCQOpDbZgAAZjoAZjo6ZjpmZmYAZmaQZpDbZrbbZrb/kDoAkDo6kGYAkGY6kNv/tmYAttv/tv//25A627aQ29u22////7Zm/9uQ/9u2//+2///bNzWMHAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABa0lEQVRIS9WW2VaEMAyGm9EBdEbBcZm6VDvSQt//CU3LItLDlHhyobmAA5SPLH9ShPif5iRAVtsCNm9MATiZ1UIYNp4Q+uIDDzmTf4ixxVG4Z66AEehkLowPm80wZnVkoyGoLW8OmEZGU3DLSEOU8XXmNMOoGS8YVs2gaPYvKx083QWxulMFsF3ULfbybpUGmwq6VCt4Ek1JSXvbi6iZisnu3kOPItAHpIGgXCe3/s223P+sfA8MNw0FiHnFTmzLeWqnQBW8VTBYYlgh8bPK56mdAP1AWbLxI9MFWKp4XHwDnaS21nmgn0/BaCFHLo4eqigbib4dijJL4gDUYc8gBN3tMnGZdVdKe4UnpwjA5qFzzfbncOFeCyzf5eOYOAKQc5D9SRZqKas1kHrzfCAKi+ckYXik8uJVollrZovr2aBK+ZB63is2tWz18/ZwTxnoSS5uevEwTb61vCB0peH7d8DJt0EPgY/4++C+ADF6GTh6V9eFAAAAAElFTkSuQmCC)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
= 6 × 2.73
= 16.38 minutes
The time taken by car to reach the tower is 16.38 minutes.
Question 17.If the angle of elevation of a cloud from a point h metres above a lake has measure a and the angle of depression of its reflection in the lake has measure β, prove that the height of the h(tani3 + tana) cloud is
.
Answer:Let AB be the surface of the lake. E is the point above h metre from A.
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)
AE = h
Let height of the cloud BD = l
Let F be the reflection of kite C.
Horizontal line EC intersects BD in C.
BF = l
∠DEC = α, ∠CEF = ß
Here, AE = BC = h
CD = BD – BC = l – h and
CF = BF + BC = l + h
In ∆ECD,
![](data:image/png;base64,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)
……(1)
In ∆ECF,
![](data:image/png;base64,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)
…….(2)
From results (1) and (2),
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Using componendo – dividendo,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
The height of the cloud from the surface of the lake is
m.
Hence proved.
Question 18.From the top of a building
, 60 m high, the angles of depression of the top and bottom at a vertical lamp post
are observed to have measure 30 and 60 respectively. Find,
(1) the horizontal distance between building and lamp post.
(2) the height of the lamp post.
(3) the difference between the heights of the building and the lamp post.
Answer:Let AB be the building and CD be the lamppost.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJ8AAAEECAIAAAC5r3GDAAAAAXNSR0IArs4c6QAAIzBJREFUeNrtnXlUU2m67q2xe1V1a3edgj63q26d7uqqPnVOnV63Si21nMABFUcUDKMCImFUVFAhhElUZhQRUCEJhBkUmSeZERECJEACYQjzECADM2TYyV36eVLIjELG/Sz+SMLeJNk/3v0+7/t9+9vrhLDkV+vgQwDThQXTfQ/Vdo7FvegfmeSJXkmtGsyrZ8KEhEJhRs1Qfj2TxxfIKt3qttFNDi8v45vA05xaxt8vlMa9oMNoazvG/t2s+F9Xy9sGJmX4zFzayP7KoqSqbYQxxv1/1156prTDaIVC4a2nbaf8a0/4EINyumU776JiW1TdqvQD6wyDydyVn4jkT+xx3oHbNXEv6A/yug951Ahkmu4kB9rpQvgLsriLMQWjFQqF6TVDu10JfEjYPjS1y4VQ1jQsw3Sb+yb+eansP6xKs0gMGC0ECayxjVscK9Kqh1KqBjdef4mOb5VVuiMTPE1/kskDyq2n7RvtyzuGFD18+1jT29AVlphG9yc096Q2DV+S2s1qxihXJuk6xrVuQ1cwxrgT09AWxwqz0EYFp/swr2ePW9UUFwJP+9nT/3XlRVr1kOzRTSin/9W8OLfuzQm5qIH1N+tS37QO0XdTuNOyQLjdqdI2skn0ikAgPH2n9pgPcZIDyRjdxy/pKYTBma+kVg3FlvVPcBSWriChnE7tHZ/5Yn3XWFRp3/g0XyZdFazVFUwXprsGmpoYKyspTHn6uKmhDsYAEmtqylNz60sGRqa+fv4DfT2ySresuGC3utZXvxr8HxXz/9h68sLFSyMshS5wORyOm5v7Fz9pfrDHc93+gE+3WKkc0qS1Nsse3dbWpv/cvO9DVY8/mZb92fT5eqOCdd8hrC7YKDLd+JjI9T9przcqVDIvVzJ/8YVF5UeqNxF6RtzpSdmiK/Dz9f5oyyUl6xolZLGSaZGSWdl644KvfzlVWvisp6en4221tra2LKWmpiYKhdKwgBobG8lkMolEql1U1dXVhEVVXl7+YlGVl5cXFhbi8fhHjx6FzqewsLCHDx8Gva2QkJDAwIBdKqqf7vdRtqp6dUBMi5SQpX84++zrracbyLWyRJfPnTaztv3s0F0ly8o338S0+Evz8g1bkac1T95wc0XPkeNSQqFQDgsL/NZ+KV2/fv3aolryL6DRaCsrKw0NjSNHjhw8ePDQ8nT48OH9e1WVv/p2w8lQZdExQRZvOFf0tapFQV6uLNEVQPzrDo6fqN5Utq4R0f3CrOKLTTrenreys7PT5ihrKeXk5OTn5+ctrIKCgpKSkuJFVVZWtnhoVlRUVC4qAoEQGBi4ceNGV1dXHA4XtoAwM4TFYvF4PD4ifO/efZ+ouClfqFFCliiZFitblH+mm/b91sPdnTQZy7s5Wemffn/oc7105Qs1ypaVytbEdSrev6qdGh8dlvX0mZub+7e//Q2DwbS3t1OXUlNTU1tbG4lEwuFwx4+q/+EfO9drx39p8VLJsvKPZ3M/+dnUycVNKIBkjC4E8R1R9r//Xv1DlVufHgpc94vtt/9SKc7PFcq+CgoKfvjhh9u3b1MoFOKiqqurq6+vT0lJsbW11dTUdHJCm5wz+rdvN370s8nHmy2VN2ldsbs2Pj4mkxWRQABlZ6RduWpvZHbJw8OjgVIvH9a3ubl5x44dJiYmDQ0NJBJpXq4kEolCobx8+TIgIODMmTN6enrBwcF1dXVenp56utpnDXQRp45lpKXIQa9KwJ2ekFpUvb292dnZJSUlM18kEonZ2dkdHR0LnJYgAwODPXv2LES3vr6+rq4uOTnZzs5OU1PTxsYmJydneHg4NzdXR0cnKCgoPS3Nz9d3bHQU7kSuoaqrqw8cOGBlZXXo0KHAwEDwYmxs7MGDB62srI4fP04ikebd0dnZ+aeffsrKyiKTyXNDtry8PDAw0MDAQFdXNzAwkEKhjI6OdnZ2otFoY2NjCoXy9OlTNze3/v5+mO4aysLC4vr160KhkE6nb9mypampicViqaiolJaWCoVCf3//M2fOTE3NM7+gqKjou+++c3FxodFoM0NWlGW1tLQuXbqUlZU1MDDAeK2MjAxtbe2goCAIghITE2G6ay4Wi8Xnvxpo6+7u/vXXX1taWkpKSvbv38/hcIRCIZlMVlFR6emZpxXM5XJVVFSOHz9eXV1dX19PIpEaGhpAyJ49e1ZPTy8gIIBKpTKZTPprdXV1OTo6nj17tqnp1VBufHw8TFdMCg8P3759OxqNFgqFGAzmyJEj4PX29vZt27bRaPMXoyEhIX/961/xeHxLS0t9fX1qairIspcuXcrOzqbT6QwGo7+/v6+vj81mp6WlaWtrBwYG8ng8mK44jb2AQCA8efLExMTkxYsXWCxWRLetrW0Rut3d3Zs2bTp27FhpaWlQUBAwxvfu3aNQKGw2m06n973W4OBgR0cHGo02NDSsr68H7wjTFbdsXiszM/PIkSMQBL0eCGndvn17e/uC8+lxONyPP/5oZmamq6sL9h0YGBgaGuqbISaTCTJuQECA6P8JpisO+fn55eXlgccmJiYoFKqrq2vnzp29vb1CoRCQZrPZ8+47NTWVnJyMQCAOHz7s5+cHHJkoZIEGBgZEgdvQ0ADTFascHR03b95cWFgYEhKyc+fO6upqoVBoZGR08eLFwsLCAwcOhIaGzrsjjUZ7+PAhGo329vY2Nja+c+cOg8EYHBzse1siq3zv3j1g32C6YhUej0cikWZmZrW1tSIj7ezsjEQiw8LC5m4/Pj6el5fn5ubm4ODw9OnT4eHhsrKyM2fOhIaG0un0gYGBmYHb2dkJrDKZTJ6Z6WG60igajfbo0SM7O7s7d+7U1dUJBK8u+eHz+QkJCdra2mFhYXQ6XZR32Wx2eno6AoEIDAzkcrkwXenV5ORkXl6eq6srCoVKSkpisVizjHdsbCzoMnZ1dTGZzKGhofb29plWGaYrpWprawsNDb169aq/v7/oBD5XqampZ86ccXZ2JhKJo6OjWVlZ2trad+/enVuDwXSlQlNTU/n5+a6urg4ODnNDdq5qamosLS3Pnz8fHh6ORqONjIwaGxthutKo9vb2R48egZBdaDhhrrq6ujAYzPnz5zU1NYOCgmZmXJiuFGXZGzduODg4PHnyhMFY2URdPp/v4+NjZWUlqnFhutKVZW1tbUGWBX2rFYlMJjs5OcXFxc27L0xXMpqYmMjPzwe17DuELBCHw8FgMM7Ozgs1qGG6EjbGJBIJ1LLvIDKZbG9vHxcXt9BfgOmKO8sWFBSAkE1KSmIy3339LD6fHxYW5uzs3NbWttA2MF3xqaOjA4Ssn5+fyBhPTk76+Pig0ejs7GzRlpmZmWg0WjTUM6/q6+tRKFRcXBwYx4XpSkzT09Mzs6yolmWz2cbGxpcvX8bj8bt37w4PD3+1LE16upqaGh6PNzQ0dHJymvesK8q4LS0ti7wvTFcctSwGg7G1tfXz8yMSiTNpYbFYDQ0N8Dg3N/fWrVt8Pl9DQwOHwwmFwp6enr1791ZWVs4buA4ODrGxsYvnbJju2rafCgoKQMf4yZMnQ0Oz1x85d+6cp6dnQECAjY1NamqqUCgcGBjYsWMH6EFCEHTy5MmIiIhZe/F4PCwWu3jGhemueciGhYVdu3YNhOzcepTP52tra//4449Jr7Vr166YmJiWlpbNmzeLeoonT56cOzhIoVAcHBwWqnFhumtujAsLC2/cuGFvb//48eOFjDGXyz106NClS5fA0/Dw8IMHD1IolK1bt1KpVBHdWaP6PB4PZNzW1qUXEoPprknI2tnZzc2yswRBkL6+fkhICHhaXl6+d+9eGo2mqqpaU1MDNtDQ0IiKipq5V11d3ZJWGaa7JsZYVMsuErIzFRYWhkAgwGMvL6+zZ8/y+XwtLS1QC1EoFFVV1ZlDthwOB2Tcxa0yTHf1QxaLxV69etXX15dIJC5zLxaLZW5ubmtr6+rqqq6uTiAQgHlWU1O7efPmvn37ZpW8IOPGxMQss70F012FkC0qKnJzcwNZdqUdYy6XGxUVFRoaCi4dACISiaGhocBFz824C3WVYbqrrM7OzrCwMNB+qq6ufodBnuWLTCaDGnc5GRem+761bGFhobu7u4ODQ2Ji4txadnW1zOYUTHcV1NHRgcFgRMZYNH947SRqTq3ovWC6Kw5ZkGXFE7Ki3IzD4ZZZ48J0390YYzAYkTF+53HZlQpY5SW7yjDd9zLGoP2UmJj4blMp3k18Pn+lVhmmuwKBqYcgZEEXSZwik8koFGpFVhmmu1ynCowxCFnxZNlZHwCLxTo5Oa3IKsN0l1XL4nA4Ozs7Hx+fta5lF69xl9+cgukuK8sWFxeDOcaJiYmDg4MS+Rg8Hg+Hwzk5Oa3UKsN0l6hlr127BkJWDLXsQmpoaABW+Z1PGzDdt2rZ4uJikGUTEhLEn2VnWeX3ybgw3dlZVjTII6ksO69Vnnt1EEx3ZZ2goqIid3f369evJyQkiLOWXeQjgYzb3Pxea90rOt3Ozs7w8PCrV6+CLCu29tNyMm50dPR7fh7FpTs9PV1SUgLaTwkJCZIyxmthlRWdbnd3NxaLBcaYQCBI0BjPFYVCARn3/T+VwtEFteytW7fs7e3j4+MHBgak6uOBucrvaZUVlG5XV5eo/VRVVSVVITszcKOjo9+hq6y4dEGWBbVsfHy89GTZWVY5PDz8/a2yYtEFHeOrV696e3tXVVVJiTFeO6usKHQ5HE5paSmoZePj4yXbflpcoubU+1tlhaDb3d0tClkCgSC1ITsz48bExKxKxpVnuhwOR5qN8bwZFwTuzFnNMN151NPTEx4ebmdnB7IsCIXp6emy15rZtu3t7S0pKZm7iJcErfLq9rfliu7U1FR6erqLi4ujo2N8fDydTgevDwwMGBoa6urqamtrX7t2bWRkBFxudfToUSQSeeDAgZmrGkikxgVWeVVqXPmk29LS4unpqaWlZWhomJeXNzMIsFjs/v37weODBw/GxcUJhUIDAwNvb2+hUJiXl6empjbvHSfEo8bGxrUIXDmhOzk5mZ6ebmZmpqOj4+rqamxsnJSUNHMDFos1NvbmJmnHjh2LiYkZHh7euXMnWMp4fHxcXV09MzNTImghCFrF5pS80W1tbfX29tbS0rKwsEhJSaHT6TgczsTEpLOzc9aWxcXFOjo6mpqak5OTdXV127Zt6+rqAidGdXV1ENDiF5lMdnR0jImJeZ9xXDmky+VyQcgiEAhvb28ikchisdhsNplMRiKR8fHxc3sFiYmJFy9eTEhIqKqq+uWXX2bSnbu9eLw9GA5aXass83RpNJqPj8/p06fNzc2TkpLAjQH6X4vBYAQEBFhbW4vOxjMVGRkJFjDYvXs3WFWEw+Goq6s/fvxYIs0pFAoVFRW1RrW47NHlcDiZmZlIJBKELIlEArfREt0kgMVi5ebmmpqaPn/+HOzy9OlT0foEWCz24MGDY2Njampqz549AxXU/v375104aK2bU2Bp5bXIuDJJl0ajeXl5nT592sLCIikpqbe3l8lkzrq7R39/f09Pz+XLlx89egT2iouL++abb7KzswsLC/fs2QNev3nz5qlTpyoqKkxNTa2trdci7S3HKsfExKzdUJXM0J2amsrIyLCwsEAgEB4eHrW1tUwmc+Z9PWbdvsXDw+PGjRvT09Ng96ysLMPXSkxMFFWZd+7cMTIysrOzm5ycFH+Ni8Ph1jRwgdLTUry9PMZGR6SFLnOIHhgYeB5pYXPZLjsrQygUtLe3+/j4aGlpmZubJycn9/b2MhiMvoU1NDQUGRlpY2Oz5HpdEm9OrWJXea6yMtKOHNP4adMWD08P5tCA5Ol2tNHUNXR//4v5OlWfD3bf/Pct2mfOGttcuKCtre3l5QWM8UIhO5Nudna2hYXFzJvzSI+4XG5ERAQajV4jq/zq3MDlenh4Kv186pN9Hr9TD/z9Lxb7j2l3tLdJki6PM6131uRTVbc/m1UomZcrmb/cYFzw4T/Ujx7an5WVxWKxRkdHWSwWcymNjo6SSCRDQ0Owioy0qbm5GY1Gr2kN9jg+5k8/nf6jYZ6SxUtli/IvzCs+2u2qf9aEx5mSGN1Gcu0/tmn84WyuklmpkmmRkmmRshXhd4fu7VBVC3v0MDQ0NGR5evjwob+/v76+fnBw8LNnz7KlRjk5OdnZ2V5eXhcvXsThcLm5uav+Frm5uZkZaUePnfhkr5eyVRU4jEpmpZ+fzf2/W7SolDqJ0c3Pzfp6i9YG4wIlZMkbuhblG07HfvPjdoSmhoGBgd5KZGhoCJaCcpIaubm5Xb9+3djY2Nra2tXV1dnZeU3e4prtP/9n4x+PP1S2rHxDF1m84VzR16qWBXk5a0g3tWrQKb711U9C69Wo5ub+iZm/7Wpv/W7r0c9005XMXyiZFishS5Staz7Y6ayrq1taUlJWVvZ82SotLS0rK6upqamvr6+TGhGJRG9v72vXruXm5pLJ5LV4i/r6+loS8ayh4Qc7nJWta17HSbGS+YvP9NK/33qkq71lDelq36076kXMIjGySQz/jI4Dt6rTqn+bDSOAIHsU+uNN5uuN8pUtK780L//0RNTXmzTKSouEcqG2tjYXF5fo6Oi1fqPnJYVfbz7x6YmoL83LlS0r1xvlf7zJ3B6FFswYhhIIhIMjnOa+CUr3OKV7nNw93tAzPjzBe3e6RiEU54Tf1n/wSes46kUcnfytnB8bHbl82fbfNp7+8BebTzab/ffOE/HxcfKBlsfjrbVVfstYJcT/a5fGR5vMPtpi8+XG09Y2V0bfrnrZE7x97tVHvYhW2EYrbKNFWKM1lkpoHXl3usYhFPuY304O/WzOL6iKfPKsBTMFSU8Sj6qrXbQyozY2COVFVCoVdJXFdoFhM7XR2tLsmLpa0pNEgWD2mzLGuL86VabXrGAm4croTnCgfe5VKVWzZxePjY36+HhnpKfLDVoIgkBXebXmKi9TGenpPj7eY2Oj83SNxri7XAjP6hhrRXeSA6m4EubS7e/vd3Nzi4+Pl/KJjMtXQ0ODo6NjdHQ0h8MR25su3mdmjb+ie+4B5W5m593MTp+0jvDi3vFp/qrRrWwd2Wj/kkAbkW+64CIDNBotWjRdeuheDKfii/vwxX3Ywt5kwsAkB3oPVxVMcU2kzYBNNgwiQ5BAvumC4aDIyEgxX9K/OF1wZs6pXb0zs2EweRu68sZj2o0nNIP79ecfUhq6x+duJk90+Xx+RETEKl4dtLp006oHV41uS/9ETi0jhTCYUjWYTBic4s7/vyxPdKlUqqOjY1RUlPgvOVycLmOU+9O18ruZnS39E+CnqW+CNc5dq06k/NEVTcAQT427Irrj03z7mBajYLJ5WMOrn9AG4xDK4idqmO48VjkqKkr8cz+kd26GfNAVjeOK2SrDdMWhpqYmFAqFx+MltfoVTHdtrbL4m1MwXbFaZYlkXJjuGgpc1ifBjAvTXXOrHBkZuaZTHmG6kglcPB7v6Ogo2cCF6a6VVQaBK/GFYmG6qywIgiRulWG6a6XGxkZglcU5jgvTFYdEzSlpWGkFprsmGVeCzSmY7lqJz+dHRkZKg1WG6a6+mpubgVWWnqVjYbqrbJUlMo4L0xWHVY6MjJQGqwzTXWWrHBkZKT1WGaa7+lY5IiJCSqwyTHc1rTIej5e2jAvTXc3AjYyMlOA4Lkx3DQPX0dFR2jIuTHcVBCZg4PF4KQxcmO57icfjRUVFSW3gwnTfS6A5JYVWGaa7CgdOaq0yTHcVrDIajcbj8VLVnILprk7GBVa5oUGqF35YhO68B3bJFKMQdEHgRkRESOGdBJeky+VyMzMzfXx8fH19CwoKwFdoaWm5e/eul5dXTEzMImcj+acrGseVWqu8ON3MzEx3d3c6nd7S0nLp0qXa2loIgm7evJmdnc1ms+/du5eQkLDQYZd/usAq4/F4yc5Vfje6o6OjHh4eL1++5HK5PB6voaFhYGCATCY7OzsPDw8LhcKamhpXV9eFljSWc7rAKkvVBIwV0W1vb3d0dMzOzg4ICLh161ZhYaFQKExLS/P29gb/rCDpgFs2KRxdmbDKi9Btbm42NzcPCwvj8XiNjY12dna1tbUpKSk+Pj4gAYP1ZxWRLo/HAxlXyq3yInSpVKqtra3o6YMHD2JjYzMzM319fUHsKi7dlpYW0JyScqu8CF0mk+nu7t7X1weehoaGxsfHk0ikGzdujI6Oghvoubi4TExMKBZdPp8PusoykXEX8cwRERFhYWHgFiIoFKqxsXF6etrBweHFixdcLjc4ODg8PHyhwldu6YJTltQOBy2fLpvNxuPxwFVlZ2eD8xCBQPB6reDgYBDECkRXNI4rKxl38V4VBEFsNnt8/K2VwiYnJ9ls9uLtKvmkK2pOyYRVXpLuO0sO6YoyLoVCEcqUYLpyaJVhuis4QNJ2dRBMdzUDVxYzLkx3Wc0pGc24MN3l1rgRERHSPxwE012xVY6OjkahULJV48J0l6XW1lY0Gh0eHi5zVhmmu7RkZQIGTPfdM67o/swwXTmhK7LK0nn7XpjuKtS4OBxOdjMuTHcxqyxzw0Ew3RVY5YiICBkax4XpLksQBMl0c0oq6FKp1OTkZDA1q6amJj09fdZEHknRBVY5PDxcpq2yhOkODg7a29snJiZOTU3Z2tomJSXN6tFLhC6fz4+JiUGhULJulSV/Zm5oaHBycnJ1db1//76UnJlBxpUDqywVeTc+Ph6BQHR3d0sDXQiCZL2rLEV0mUzmrVu3zp8/n5mZOReh+OmKusqyOI4rdXQxGIyfnx+RSLS1ta2trZUsXdHMKbnJuJKkSyAQ7OzsWltbhUJhYmKiq6srg8GQIF1glXE4nBzUuJKnOzIywmazRQlvcHBw1mEVJ10IgoBVlo8aF+5mvCUajSZnVhmm+5vkpqsM052tlpYWJycnuWlOwXTfssqgxpUzqwzTfVPjOjk5YbFYGZ3yCNNd2irLa+AqNF2RVZazGhem++prg4wrfzUuTPeNVcbhcHJplRWarmgct76+XijXUkS6IOPKsVVWXLoCgUBeu8ow3d+ssjyN48J0hTMnYMhxjau4dEVWWRECV7HoQhAUGxurCFZZEem2tbXJd1dZoekqjlVWOLpgOAiHw01NTcF05Yqu4jSnFJEujUYDGVeOh4MUlC4EQXFxcQ4ODooWuApBV2SVFS1w5Z+uqKusIM0pxaLb2trq7OyMxWIVyiorBF0+nx8bG+vg4FBXVydUSMkzXZBxw8LCFDDjyjldkVVWzIwr53RFVllBhoMUiK5orrLCZlx5piuyyvI95VER6YKMCweufNJtb293cnLCYDCKM46rQHRhqyy3dIFVxmAwitmckme6oDmFQqHmLqID05V5ujQazdnZGYPBKHKNK590wTdR5K6yPNPt6OgAgauwXWV5pguGg2CrLId0RRkXtsryRlc0HARbZTmk29bW5uzsrMjjuHJLF3wBuKssn3RFXWW4xpU3ugKBQMFnTskzXRqN5uLiAltlOaQLQRBoTsFWWQ7pgowLW2U5pCvqKivg1UHyT1fUVVbwmVNySBesgIFGo+HAlUO6DQ0NSCTS3d19bGxs8b/T19dnbW1tZGQUFBQk+lMPHjwwMjK6cOGC6M4bMF1poQtBUHBwMAKBMDExuXHjBolEWuiP0On0EydO+Pv7V1ZWHjhwwMXFRSgU4vH4I0eOVFRUODs7GxkZwauAShddKpVqZGTk6OiYmZl5/fp1AwOD5OTkeac/BgYGGhgYgMcUCgWHw/F4vKNHj8bHx4O75hw6dCgvLw+mK0V0AwMDtbW1MzIyxsfHOzs77927p6ure//+/fHx8VlbmpiYODg4ODs76+jo+Pv7g3uH7tixg0gkgg0QCMSjR49gutJCl0KhgMBtb28fHBwcGhqi0+lPnjzR19f39fWdeRNfCIL09PS+//77yspKKpWqrq5++/ZtGo22efNmkRdDIBAhISEwXamgy+Px7t+/j0AgUlNT2Wx232vR6XQ2m52enq6np+fn5yfyWRAEHT58GI1Gg6eZmZmqqqoUCmXHjh0z6QYHB8N0pYJuY2OjoaGhg4NDZ2fnwMBA3/+qv7+fwWAkJycjEIjY2FjR9ubm5r6+vuAxgUDYs2dPV1eXmpra8+fPAf5Tp05FR0fDdCVPVyAQBAUFIRCI9PR0BoPR97YGBgaYTCYWi9XT0yMQCGCX5ORkNTU1YLhQKJSZmZlQKDx//ry9vb1QKCwrK1NRUQF3moTpSpgulUo1NDREoVAg4/bN0eDgYGdnJxqNvnr1KpPJFAqF09PTnp6eBgYGpqamp0+fBiDJZLKGhgYSidy5c2dCQgJc70qerkAgCAwMBIHLZDL75lNvby+LxSISiUZGRomJiaJ/CwKBUFpaCngDDQwMlJSUKEKfSzbokslkIyOjRQJXlICHhoZCQkKQSGRvby/ciZR2usD+iKwyi8XqW1QMBqOuru78+fPybZfkh25zc7PIKtPp9MXp9vf3M5nMgIAAa2vrmeUvTFfq6IL0CbrK81rleQXKXxMTk/Lycpiu9NJ9+vRpQ0PDuXPnUChUW1vbIhl3puh0ekdHh42NDQaDgelKI93xsVE/X5+M9LQHISE6OjppaWlLZtyZYjKZt2/fdnd3h6fBZqSn+Xh7jY+NSgvdsdHh+4H3du7apX74yPGjR9xcXbq6umY2p5bU0NBQRETElStXurq6FBltSVHBaQTi11+33w+8Nz46LHm6fb09WrqGn28+98l+r493u3zyzU5zC8vhYXZ/f/+K6GZlZZmZmSns5A0Igu4FBHy16cTHu50/2ef12aZzJ06f6evtkSRdPo97Dmn5u12OfzItV7Z4qWRRsd4w98uNp6PCwzgcDmvZGhsbq62tNTIyqqqqUky6qclPvtyo9bl+ppLFS2WLl39Gln+0HWWCtOTzOBKj29xI/m7bic/P5CiZPVcyLVIyLf6LddXH+3z3HjiCD8dFRETglqeIiIigoCB9ff3Q0NDS0tIiRVJJSUlB/rNTpzQ/Vr2tbFWlZFr86kiaPf/8TM43W061UCkSo5uXk/n1Fq0NxgVKyJLXdIuULco3IOK++mGrpsYxfX193eVJR0dHV1fXwMDg8uXLLi4uaEWSq6vrNbsr//zx5/UnHipbVoLDqIQs3nCu6CtVy/y8HInRbW9t+nbL0c/0M5XMy/43dqs/3H3jlKZWbk52Xl7es5UoLy+vvLy8qqqKoEiqrq6urHipo6f3wS43ZevqN7FrXva5fuY/th5ra6VKjC7E59tctvtoi82Gc8VKlhVfmpf/XivxLz9rFLzff5wCKv9Z9l9+1vidVuKX5uVKFhUbzhV/tMXG5rIdxOdL0jOzWIzzSIv1P+us23R53Sbrb7cew2KxMK13UEQ47rttx9dttFq36cr6n3UNTcxZTIZYPXP08/7LeOq16ObEl/QZzpmTlpLs4+URHBRIItbAnN5ZdbXE+4EBft6eaakpHM5bc3tr2kadElodYltQcS2XIqjp1UOrSXdwhHP+IeUijppeM5RFYhz2rHFJaOXwIBiJeBSU0/Wfl8tSqwdzahkRxX1bUBW5dYxVo+v+pE3DlzQ8+WYeMoE2csybWNsxBh938ehRfs9hT6Lo6ZmgektM4+rQhQSCk74kbNFbA+ydjCn2BA8+7uJRaH7PvpvVjDHu+BS/fXBS0782i7RKscuDBCquhJjn/fBRlpTCi3q/vfj8TFD9uQcUTT/SD5fLShvZq0OX/5pueBE8OUaSsbv/Vs3wBG+aCw1P8CwxjSd8SFMcaHXyru69eq/Ujt/O1ZAQFdvyrI4JH3ex0T14u4bDfzO3MLeOudu1irVUZlwu3dSqwZ0uhJq2N+OOj/J6/n6htKJlGD7uYnJVeT3qM1yVZ3L72fv1qxa7fEhwJ7NT1a3KIbblCr5ptyshtWoIPujijN2/X3iOim1xSaRdwFGPeROpveOr3M2ooo08JQykVg22DU7CR1ycGhjhFDewUqsH06oHkyoHOoeWtSTUOvjAybFgujBdWDBdWDBdWDBdWDBdWDBdxdX/B4dHQKel+deNAAAAAElFTkSuQmCC)
The height of the building AB = 60 m
Horizontal line DE intersects AB in E.
Let BE = CD = x
AE = AB – BE = (60 – x) m
∠AED = ∠ABC = 90⁰
Now, the angle of depression of the top D and then bottom C of the post CD are 30⁰ and 60⁰ respectively from A.
Then, ∠ADE = ∠XAD = 30⁰ and
∠ACB = ∠XAC = 60⁰
In ∆ADE,
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGUAAAAqCAMAAACdrGVEAAAAAXNSR0IArs4c6QAAAI1QTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOgA6OjoAOjpmOjqQOmaQOma2OpDbZgAAZgA6ZgBmZjoAZjo6ZmY6ZpCQZrb/kDoAkGY6kLyQkLbbkNv/tmYAtmY6tmZmttvbttv/tv/btv//25A625Bm27Zm27aQ2/+22////7Zm/7aQ/9uQ/9u2//+2///bRKOwNgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAB7UlEQVRYR+1W2VLCQBDcDUqUK55ZlKAigsQk+/+f50zvJBFFqohOlaXOQwjXdLa75zDmP/Yx4N3xhr73zoZIVejKbTTjxFXSp+tLrIOSXccTRvGOUUymglKdL2rKgKITy75Z9h7rs6x0kLxLTQEtgvw6KMVwI4pAl1wHZQn3MmWivoYu1Rm7OOciUUTJUZEoFT0nS+YqIcpCVQYnfGtUibV0GH7pLaTDhEbwR8KvTq09won91NrhQ+dzFyef85ZFt6Z0TCx389KhcXSKfI86GZtkyd7Hr1AFnWIeKhXcjDmRTZ9ivmsi4xPgEqzZKfCUZPONz/iuiAez8PghyumI1Ajjr0pQcl2iZQz1IxeMIc5r7YgyBxQZtYKSycC1Mhr3gu9CqRJBoX+uYyJrF8rOrA3y1o3oavz6MsYegLO8RSGpJg1jX9elJus9SsFTXNRvj0gfHcwYaGt1kbN4x1nh32Dnzk6m3BNzd0OX8orJQiY8PqtN4GVjr23xD3Ta3EapobIZPyc2LVgddhZgyim9HcO95UVw24+IsFFEg3tQobZcoj+UDlzoLZdhWEJR/ZFcxO3gV5CyGfzUknCvslwKClyvt1xuo2gtlx8YU1Cl8RW6h95yWS+Uuk6WqqSmVVelwnIpHYaneNNhftdy+Qqe/jHeSZwNNwAAAABJRU5ErkJggg==)
![](data:image/png;base64,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)
DE = √3(60 – x) ………(1)
In ∆ABC,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
…………..(2)
Now, BC = DE
From (1) and (2),
√3(60 – x) = 20√3
60 – x = 20
X = 40
1) The horizontal distance between the building and the lamppost
= BC
= √3(60 – x)
= √3(60 – 40)
= 20√3
= 20 × 1.73
= 34.6
2) The height of the lamppost
= CD
= x
= 40 m
3) The difference between the heights of the building and the lamppost
= AB – BE
= 60 – x
= 60 – 40
= 20 m
Question 19.A bridge across a valley is h metres long. There is a temple in the valley directly below the bridge. The angles of depression of the top of the temple from the two ends of the bridge have measures α and β. Prove that the height of the bridge above the top of the temple is ![](data:image/png;base64,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)
Answer:Let AD be the bridge and E be the top of the temple.
![](data:image/png;base64,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)
The perpendicular from E on AD is EF.
Thus, EF represents the height from the top of the temple to the bridge.
Let EF = x and DF = y
AF = h – y
In ∆ABE,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
………(1)
In ∆DCE,
![](data:image/png;base64,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)
………..(2)
From (1) and (2),
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIsAAAAqCAMAAAC0h1iGAAAAAXNSR0IArs4c6QAAAJlQTFRFAAAAAAAAAAA6AABmADpmADqQAGaQAGa2OgAAOgA6OjoAOjpmOmY6Oma2OpDbZgAAZjoAZjo6ZjpmZmYAZmY6ZpDbZrb/kDoAkDo6kGY6kLyQkLaQkNu2kNvbkNv/tmYAtmY6tmZmtpBmtrZmttv/tv//25A625Bm27Zm27aQ27a229v/2/+22////7Zm/9uQ/9u2//+2///bP0C6TgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAACBUlEQVRYR+2X21bCMBBFM61IBKF4gXqloFBBbUPz/x/nNInFCybRDK4+MA+li9DNyck0M2HsEOEOZACdIgeYBKFoKCyLpkymYVIYEUWm6MswyBV8mIbCBD8dhEphRBSW4yqFBwmlOr+Il8FaSCjyalol3VAtJBSZYd6WEJi8JBSZQoS+QJgYGkro2riez3Gqrt/823h50LLT63b5cj8LfDPI8qmE/kLW9bcFUdbdiLqQBDYnJv4wPZUvghstX1EN2XrjmoUv5bMWF3W/48RaCNdov/N20Ylz1/V3tvESsCAJHtrbh0iQDxyicQiB7tksXrCVTx8iTih2QRulSrA3k6lHt0hTrmwUNeajBUsVQLyUqx4AHkYwuyZPvL5TIUZwhI2es+e0UtSZwAOC/25UF7pmCd6fstxUDMHHbBU/emz2NkqOB4vNaFC4E3DrrqoT5qKdyDoFmtv71Up/p6CWHI5f3FK0L3pBGi3GUP3xbpKVZaGw2hc5izyKs6bI9ZnegpSgT1pKNMcZForSoj12RbPSP/mS+ZwjLRSjRSuyh6Js6+dHX9R7WI08UlcDdlPMCd1nSoIP2fwGL5vLenlU9aq/qwPfRjm/S4bPzilZKdAt2Nog7cbMANMKN4jBawITVbiak6O8xu0FxzzeRwslj297balHPpniyiSq8YOW3U62yZdG4RuN4zxmd/GK5QAAAABJRU5ErkJggg==)
h tan α tan ß – x tan ß = x tan α
h tan α tan ß = x(tan α + tan ß)
![](data:image/png;base64,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)
The height of the bridge above the top of the temple is
.
Question 20.At a point on level ground, the angle of elevation of a vertical tower is found to be such that its tangent is
. On walking 192 metres towards the tower, the tangent of the angle is found to be
. Find the height of the tower.
Answer:
Let AB be the tower.
![](data:image/png;base64,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)
The angle of elevation of tower from D is α and on walking 192 metres towards the tower from D to B, the angle of elevation of tower from C is ß.
CD = 192 m
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Let BC = x, AB = h
BD = BC + CD = x + 192
∠ADB = α ∠ACB = ß
In ∆ABC,
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![](data:image/png;base64,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)
4h = 3x
…..equation (1)
In ∆ABD,
![](data:image/png;base64,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)
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12h = 5x + 960
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36h = 20h + 2880
16h = 2880
H = 180
The height of the tower = AB = h = 180 m.
Question 21.A statue 1.46 m tall, stands on the top of a pedestal. From the point on the ground the angle of elevation of the top of the statue has measure 60 and from the same point, the angle of elevation of the top of the pedestal has measure 45. Find the height of the pedestal.
Answer:Let AB be the pedestal and AB = x
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)
BC is a statue and BC = 1.46 m
The angle of elevation of the top of the statue C from D is 60⁰ and from the same point the angle of elevation of the top of the pedestal B is 45⁰.
In ∆BAD,
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEAAAAAmCAMAAABDGm2rAAAAAXNSR0IArs4c6QAAAHtQTFRFAAAAAAAAAAA6AABmADo6ADqQAGa2OgAAOjpmOjqQOmY6OmaQOma2OpDbZgAAZgA6ZgBmZjoAZjo6ZjpmZmYAZpCQZpDbZrb/kDoAkDo6kGY6kNv/tmYAttvbttv/tv/btv//25A627aQ2////7Zm/9uQ/9u2//+2///b21xhZQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABLElEQVRIS9VW7W7CMAxMWiAMBtvYB9kolK5Nm/d/wp3TUImKVU4ipM1/WiF8ubOdc4X4d1FIOa8rKffRzIvsIKyOz0cyGGyiz0eiUavHlHwhKohIie71LT8nANjPQ7ddxAPYAgVsZHQVrZYZGMh4hHjuU5nfu6S+tC8yqS1mfaqSAKDt7wHgzvtgTj1LwgB6/eK6ywKYmoMxwH0kTDJg1uo2hv1SKMvs4z63ZIRKhoqfcKcR2fIYfGgDM6AkZ0mtDjeF4l05K7KaPM3q0Np1z+VFgzNFowK9sVr4mesZQIkrCTtooRlFS80D+JqyAcxDPah3DEIBsJMRZD5xEronamFDi90DmL4n3GhcxdwIeADa9PwYaEODH6Qs5CuBthEo0CMv+1Fen/jH//7PH9p2FQUhTllpAAAAAElFTkSuQmCC)
AD = x
In ∆CAD,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
√3x = x + 1.46
(√3 – 1)x = 1.46
(1.73 – 1)x = 1.46
0.73x = 1.46
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEoAAAAqCAMAAAAj+j0ZAAAAAXNSR0IArs4c6QAAAIpQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOjoAOjqQOmY6OmaQOma2OpC2OpDbZgAAZgA6ZjoAZjo6ZjpmZmYAZmZmZpDbZrbbZrb/kDoAkDo6kGY6kLaQkLbbkNv/tmYAtmY6ttv/tv//25A627Zm27aQ29v/2////7Zm/9uQ/9u2//+2///bYcmn9wAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABx0lEQVRIS+1W21LCMBBNikLEIhWvRKQRC/aS/P/vubm0JFam2aIPzrgPDJmmp9lzTnaXkD8fh7vcz6FI3FK9sWmJya5Z0cm790LNHFTFFh8YIFKnu8KHktmjharYMwrIbA6gxLIyUDKb4ZECqGpeWqiKrs+Dkrc5sVBi8rqidIGi3U9Q8SWcJ8mLteL0piQHBmtMHLmqqAuAMj4QODeEtJtTEeKgAkUijvdlf8uVNhv6VKH61u01m5Vkj5JRbRjwc/HUGQn4slgg4OU2Iqn/Lb/CgKB0WhYUJeapgwhQVPExt7uHqJ1fBJcRDuqirbixfNTsejG8t4M/+ccUR+zHT35Y3j8E5Z+MTlC95OPKc591oeshRRbBb1PkcL1lRn8Ea1g8t0NtKJ3v3AJMrQPKsNpfQZEJ2vYQpPZfw1uBhPZ0zeBXJFvScJQJTPkNm54p0EJ31AJ18YR+L9BaZp1Y5mFs2M4iM69JddZuNmnLYQychXKtyryguB0WtP4ppjn3oTzeDmxMgsexxW99OI872juma39MCBaDfBm9vaScaGYQQU5GWjxDmDVE6wSl3dnYGSQ6YBY1SlkoOzBANLprY8er6I+evfETPR4nITFYCOUAAAAASUVORK5CYII=)
X = 2
The height of the pedestal is = AB = x = 2 m.
Question 22.On walking ……….. metres on a hill making an angle of measure 30 with the ground, one can reach the height of 'a' metres from the ground.
A. ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAC8AAAA5CAYAAACmqHIqAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAK7SURBVGje7ZqxThtBEIbXPfQgMXSkJ6trU0XHitAG5by6Dlyg00oIJBcUa3cuyAtQhZJngDKNHwEpPAF+BjvMnS85493Dhtv1rORimzvb+m797z//jM36/T4LdQULvobPP4Sx1qKLIvxk0UUVfrzIIgkfpOanWg4WfhI6/DhY+DrrJAtv0rtWYp8DGxbuAiMeZ6dU4Wf0juCRkOedwWBjMOhsSAEa73PZO6IKn+sdYdM4Pa7ex2tihz0w3r4lCV93v4SHOLsgBb+Iv1+dff0MvP2TnObr/L3b7WxmSZQAg8c4yb55h3/L7mz+rnW6zRn7M80y+QN6lU0picpqLav3nlJbksN18X7+lGq97Qu+mgTn5LFMnmlzdot+L5Te9675ygO03pNnepIfrQzeBGvTu+mM5PAg7rFwrQp+ZvdNu47VFRgb7fKDm+9nV5/wtUqKQwD47WLXl7LK6gOY4POCBOz+/1mBZ+DyWqneFgmfd9WL+oIfrzK/f7jCUgFvrAF3AlZxLlulJweNuUiK6PzFuZ7xW8ZoURS6+SpNDjzP/8CHidJ7eE3F/ASAPZp6AjLg/xqXVwWtqNDmbsyaJF0uE3wWw4UpRtTFi7pA5mxZYvSTKTrnet8RD6Z4QUIytt0tJWPrB0jAF5KZdROtkj0BcFeXSAnBs0mUZEkZ6HisTkrJpGl8XLoPOfiZUPdik0KqQ7wuOfuFAU8k+ktQFTboeOBj6NTyNVRtFL6Yy7BREZFhhMOlTre7SR5+6r/juSmDpZiQgS+cAe4iqX6U1/JetUiBzibCjcBjo22yrroARd5tTFUyGHishq5mkk7hi5kNH/rc9UbgywPsarDkFB7bNJ+HtDF4PKSvde6z0n4AnJ/iz5TVeIAN9MEuv/Gl/ffu+KX1bymOfvlrBH7aOFj70yCL1DrPr+EDWX8BkV4EqGCDXiQAAAAASUVORK5CYII=)
B. ![](data:image/png;base64,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)
C. 2a
D. ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAA0CAYAAACKJRg7AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAGkSURBVFjD7ZaxbsIwEIavOzwAEu7GA6BT1o6phTpXNVY2yBRZqqiU0bBl6Qt0KiPPAC/AI3TgCeAZoDlCJJomNm7pUMmRToou0pfz3fn+g9lsBtc08EAP/E/A/Lkhq747A9M0bksePDOAbQ7ZszCZDBHmALiJtO44AQnGu7AChmuhdI98KsQRY/ABOJw7RZhlcauA8WWcZa3SP5X4kEd6QDl9cAImIZsAsB1Xun/uL4Df/Uag1lEHATaUr+q3Y/66fHUetRXYFEV53LofGYHFcb9WUSvR44wtTMe1AOEQiERQvynJBxiqUXncKAofy6pfBDxWmMGS+o5ahks1IL9EeM8j3HKh7/xw8MC/ApaD08VswL2r+aJ4oEHgTeJ+MTARgcgFfkfTm0Y/w+FrnKbtHwFPglRt5INJ8SwSwBaBVE+lj3TltI40inyzLiver9MN29bgXOU6ef0VkGTUJPJOQEoDA1yborsYWBbJtDE4AWknNBXCCUiFqObNdGMsMBxjmIzPrx5ttfe3+NaUS1NkL8WVq7GGddi2fTXqyNUa20/sWvsEkUrRBDqcu/wAAAAASUVORK5CYII=)
Answer:![](data:image/png;base64,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)
Suppose on walking h metres, one can reach the height of “a” metres from the ground.
![](data:image/png;base64,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)
![](data:image/png;base64,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)
H = 2a
Question 23.The angle of elevation of the top of the tower from a point P on the ground has measure 45. The distance of the tower from the point P is a and height of the tower is b. Then, ……….
A. a > b
B. a ∠ b
C. a = b
D. a = 2b
Answer:![](data:image/png;base64,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)
From the figure we see that,
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFkAAAArCAMAAAAkP9RXAAAAAXNSR0IArs4c6QAAAI1QTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOgA6OjoAOjpmOjqQOmaQOma2OpC2OpDbZgAAZgA6Zjo6ZmY6ZmZmZpDbZrbbZrb/kDoAkDo6kGY6kLyQkNv/tmYAtmY6tmZmtpA6ttv/tv/btv//25A625Bm27Zm27aQ2/+22////7Zm/9uQ/9u2//+2///bErgCqgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABcklEQVRYR+2WbVODMBCE70AbrdZifQlWaNWmKgT4/z/PuwQI6lgFg2Nneh8YZlqebJbNtgCHURhuRnJBHcgdZ1X4tMTgZgSvVXD+CAqlf7QKEoAymoxANtlIjzPvaJu6PSNbn+fezaBYTLLqgfG+R10sEY9GAA8VuvWqxUQftECafvbpk51CtKjJ/c9rvlNIGV0PJa94l+Gmej5FnAHkiHIr+M5OOrcrazFQcxVTClNmaDFNXFflZ9kvyUaf0VVf7BkqLxNoyFPxIaYp79bMF346nx25Pp1VTAvQ50pCdXcLRfx9NtrV0DxJ6qqXBeWq0VyTyXQ7tcda9KoDQ2afO250G6WTnfeF/jM3zOOf3DBeW3LKantq5q+v7+lSXPEbzK0lbtv2DHJuirjnf4kVBhIo1rPXCCWfYllGiA2avGZ0sSC76bfzMP/EgaaAvMtxBeQd3RbQHpHbAvKt2RWQb7IrIN9kbhxbQN6nKSDv4L8AvgGoMCJcB7MtMgAAAABJRU5ErkJggg==)
![](data:image/png;base64,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)
A = b
Question 24.A 3 m long ladder leans on the wall such that its lower end remains 1.5 m away from the base of the wall. Then, the ladder makes an angle of measure ……… with the ground.
A. 30
B. 45
C. 60
D. 20
Answer:![](data:image/png;base64,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)
From the figure we see that,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
But, ![](data:image/png;base64,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)
θ = 60⁰
Question 25.A tower is 50√3 m high. The angle of elevation of its top from a point 50 m away from its foot has measure
A. 45
B. 60
C. 30
D. 15
Answer:![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANoAAAD+CAYAAABcIBv7AAAPhElEQVR4nO3df2xV9f3H8XZOArWUn5dNZLJ9q0SxYJzTLdtY+Cbd+Cpkbg6nfIul9/bejirVlpQvKqLfo+VryyRrbUJqorGFEfhrJXUGFhzfRmopBhIjimnjDcofbWJM6j/kaoJ57495ms/9ce69vef3Oc9HchIptT1t79NzXrcFywSA7crcPgEgDAgNcAChAQ4gNMABhAY4gNAABxAa4ABCAxxAaIADCA2hV9M+KpHEsOwf+tS290FoCLUjI1MSSQxLbccFqe24YNv7ITSEWl3vRantuCD7hz6VSGJYzk58acv7ITSEWiQxLDsPjWf9s9UIDaGVeRWr670oNe2jtrwvQkNoZe4yfa8dGZmy/H0RGkLp7MSXOZ9prGkflbrei5a/P0JDKO08NC6RxLDhYTVCQygZXbn020erv6dGaAidQluspn3U8u+pERpCp673Yt7bQ/220srvqREaQieSGM77hIf+RImVT4oQGuAAQgMcQGiAAwgNcAChIbAGBwdl11N75Le/f0j2798vp0+fdu1cCA2Bc+nSJfnF+lqZW7lIFt/bIPNqNsu8ms1SFVkhLS0t8s033zh+ToSGQLl27Zr84EerZOm6x7N+rGpp9B9SteYB2fzIVsfPi9AQKH9qflyW/+T3eX+OccHyVXL48GFHz4vQECjfX7FSFj90KG9o83/1P/JwXYOj50VoCIzPP/9c5lVW5Y0skhiWxQ//VapvW+PouREaAuPatWtSXl4uS2On8t863rdf7rx3naPnRmgIlNtq7pLKX7blDa3ihz+TP+1oc/S8CA2B0t/fLwtuut0wskV/eF3Kv/MduXTpkqPnRWgIlFQqJXff81OpuGmtLHrwtbTIqmo1mbfge9L18l8cPy9CQ6AcP35cNE2T+++/X+bMrZB5C5dL5cp7ZE7lIrnx5lvkxIkTrpwXoSEwxsbGRNM00TRNjh07JiIiTz31lGzZskVee+01V8+N0BAIU1NT0tnZKZqmSXd3t6RSKRER6e7uFk3T5Pjx466eH6HB91KplPT19YmmadLZ2Skff/zxzO8RGmARfZdpmibDw+l/FwihARbItctUhAaYZLTLVIQGmJBvl6kIDTAh3y5TERpQokK7TEVoQAmK2WUqQgNmqdhdpiI0YJaK3WUqQgNmYTa7TEVoQJFmu8tUhAYUoZRdpiI0oAil7DIVoQEFlLrLVIQG5GFml6kIDTBgdpepCA0wcPLkSVO7TEVoQA6Zu6zUW0YdoQEZrNplKkIDFFbuMhWhAQord5mK0IBvWb3LVIQGiD27TEVoCD27dpmK0BB6du0yFaEh1OzcZSpCQ2jZvctUhIZQcmKXqQgNoeTELlMRGkLHqV2mIjSEipO7TEVoCA2nd5mK0BAaTu8yFaEhFNzYZSpCQ+C5tctUhIZAc3OXqQgNgebmLlMRGgLL7V2mIjQEkhd2mYrQEDhe2WUqQkPgeGWXqQgNgeKlXaYiNASG13aZitAQCF7cZSpCQyB4cZepCA2+59VdpiI0+JqXd5mK0OBbXt9lKkKDb3l9l6kIDb7kh12mIjT4jrrLOjs7PR+ZCKHBZ9Rdpmmap3eZitDgK+ouO3nypNunUzRCg2+ou6y/v98Xt4w6QoMv+HGXqQgNnufXXaYiNHieX3eZitDgaX7eZSpCg2f5fZepCA2eFIRdpiI0eFIQdpmK0OA5QdllKkKDpwRpl6kIDZ4RtF2mIjR4RtB2mYrQ4AlB3GUqQoPrgrrLVIQGVwV5l6kIDa4K8i5TERpcE/RdpiI0uCIMu0xFaHBcWHaZitDguLDsMhWhwVFh2mUqQoNjwrbLVIQGR4Rxl6kIDY4I4y5TERpsF9ZdpiI02CrMu0xFaLBN2HeZitBgm7DvMhWhwRbssnSEBsuxy7IRGiyVSqWkv7+fXZaB0GApdlluhAbLsMuMERoskbnLpqen3T4lTyE0mMYuK4zQYBq7rDBCgynssuIQGkrGLiseoaEk7LLZITSUhF02O4SGWWOXzR6hYVbYZaUhNBSNXVY6QkPR2GWlIzQUhV1mDqGhIHaZeYSGvNhl1iA05MUuswahwRC7zDqEhpzYZdYiNGRhl1mP0JCFXWY9QkMadpk9CA0z2GX2ITSICLvMboQGEWGX2Y3QwC5zAKGFHLvMGYQWYuwy5xBaiLHLnENoIcUucxahhRC7zHmEFjLsMncQWsiwy9xBaCHy/vvvs8tcQmghMT09zS5zEaGFALvMfYQWAuwy9xFawLHLvIHQAoxd5h2EFlDsMm8htIBil3kLoQUQu8x7CC1g2GXeRGgBwi7zLkILEHaZdxFaQLDLvI3QAoBd5n2E5nPsMn8gNJ9jl/kDofkYu8w/CM2n2GX+Qmg+xC7zH0LzIXaZ/xCaz7DL/InQfIRd5l+E5hPsMn8jNJ9gl/kbofkAu8z/CM3j2GXBQGgexi4LDkLzMHZZcBCaR7HLgoXQPIhdFjyE5jHssmAiNI9hlwUToXkIuyy4CM0j2GXBRmgewC4LPkLzAHZZ8BGay9Rd1tfXxy4LKEJzUeYum5qacvuUYBNCcwm7LFwIzSXssnAhNBewy8KH0BzGLgsnQnMQuyy8CM1B7LLwIjSHsMvCjdAcwC4DodmMXQYRQrMdu8xaXV1dUlZWNnMkk8lZv476+0ePHnXkvAnNRuwya+mBnDlzRkREzpw5k/ZrEZGjR4+mxZX562QyKRs2bJh5/erqakfOndBswi6zXllZmXR1daW9rKurKyuczNfZsGGDNDc3iwihBSq0VCol+/btkx07dsiePXvYZRbIdfVSXy7y74hyvU5XV1daUNw6BsTrr78u8XhcotGoNDc3y5UrV9w+Jd8rFFoymUz7Z5V+++gmQrPYO++8MxNZLBaT+vp6aW1tLSk2/QHi9H99vSrX50C/OiWTyaw9pisltKtXr1p6HDhwgNCsMjk5KU888YREo1F57LHH5L333pPnn3++pNhyjfiwx9bc3Jzzc2J1aG+88YY0NTVJIpGw7IjFYhKLxVz/+vk+tFQqJS+88IJEo1GJx+Ny+vRpmZyclMnJSenu7pb6+nppamqS8fHxot5erlGfuTXCSI+trKxMqqurbbl1fPHFF6W+vt7S0BoaGiQajUpvb6/Vn5JZ8X1o+i6LxWLyyiuvzESWK7ZCVzajUW/0QAoz9T8+xT4ZUoge2vnz57O+jqUeTz75JKGZpe6y3bt3y+XLl3N+sru7u2Xbtm3y9NNP5317RkEZPZDCItfT++pT9yKFn94vBqF5UK5dlu8T3tLSIo2NjfL2228bvs3MJ0Eyj7CGpt826tQnQoxelut1CiE0j8m3y4yOkZERefTRR/PeQhqN+rBf0UTSN5rR7irmx7TyITSPKbTLjI5Ct5BGt45G30uCtQjNQ4rdZbmOZDIpLS0tEo/Hc95CGl25jK50sBahecRsd1m+W8jW1lb54osvst5HdXV11oBvbm4O/dP7TiA0DyhllxkdL730ksRisZxXNf3qlfmT6m5/wzMMCM0DSt1luY7z58/PXNVy4Uew3EFoLjOzy4wOfauNjo66/eHhW4TmoslJ87ss1zE0NCQNDQ1y8OBBtz9EfIvQXKLuslgsZmqXZR7JZDLv7SOcR2guOXz4sMTjcWloaDC9y4xuHxOJRNE/cAx7EZoLzp07N7PL2tvbLdllmUdfX5/EYjF588033f5wIYRmu6+++kpGR0dlcHBQrly5ItPT0zO7bPv27Zbtsszj1KlTsm3bNnaaR9gR2pYtW2T9+vXy3HPPufqxuR5a685dUl5eLgtXrJab7lgnNyxYKt9fsVI2btxo+S7LPNhp3mJlaLuf2SvXffd6qVi8Qqp++BOZWxWRZctXuvYnrV0Nbe1d98jimvtkyda/SSQxPHPM/9Uuue76udLY2GhbZHpoW7dulaamJrl69aqbnwqIdaH9+r5NsvTWn8nihwbSHlcLfrNPFiz7gRw4cMDxj8210HbtfkaW1fwm7ROR9kn5ry5ZErlRxsfHbY1N/5O4hOY+K0J7+eWXZcnKNYaPq8Wb+6W8vFw++OADRz8210KbW1Epizb3G35CIolhmX/HJtm3b59cvnzZtmPXrl0Sj8flk08+kVQqxeHioWma1NfXy9mzZ0v+ev7HqtVSuW5X3sfVnJU/lx1PtDn6eHcltI8++kgWfm9l3k9GJDEs89c/LbfevsbSv0PC6C9v2bNnz8zfbszhzrF9+3ZpaGiQxsbGkr6WjY2NUlZWJpHGt/M+rhY+cFB+/NN1jj7mXQltdHRUltx8RxGhPSM3/2jVTAx2HfF4XPbu3ev6Ay3sR0tLi6mvY11dnVw3Z27Bx9XCBw7KLbevdfQx70poX3/9tZSVl0uk8Z95PyFVd26WaDQqb731lq3HqVOnZGxsjMMDh9mv5eJly7OeBMk8Kn/RKlsejTr6mHdto9236QG54e6o8Wh95JjMmVsh586dc+sU4UOPt7TKkrWb8oT2/7Lwxlvk2LFjjp6Xa6F99tlnUnFDpcxf154d2R//KnMql8ievZpbpwcfq161Wm64J571uFpa/3epWn2/PPjItqx/p7bjgmGcVnD1+2hjY2Ny5933ypJVv5SKu+ql8udPStXqjXLdd6+X/33x/9w8NU+KRqNZR09PT9rrDAwMpP3+xMSES2frnmQyKf/5640yp6JKKtY+IvNu2yQL1vxO5i1YZvhsY23HBantuJDz5TXt5v8oVUmhZRa/85C5H8odHByUZ599Vjb/d1ReffVV+fDDD029vSCamJgoGM7Q0FDa62T+OmxOnDghHR0dsvnhOun881/k3XffNXxdo9COjExJJDEsR0bM/e+/ZhXazkPjOd9pJDGc8yRhnaGhIWlry/+9n7a2NhkYGEh7maZpWVc9ZCsU2tmJL029/aJDy1f22YkvJZIYlv1Dn5o6GRjr6enJG4x+xRsZGUl7+cDAQMFAkf/W0ewdm8gsQqvrvZj3qnVkZMr05RXGNE2Ttra2tP2lXr1GRkZy3ibqt4/IL9+TIXW9F02//aJDq2kftaRslCYajaZdmfQrmB6b0R4jtOIYXdH0uWT2bq3o0Kx40gPW0p9hFCE0s4xCE/n3RcbsVY3QfEy9XeTW0Zx8odV2XHAuNCuqhrXUuHgyxJxCVzSzFxnLngyp671oyTf2kK3YiHh6v3SFNppZRYemP4Wf7+l9bi3to2la2i2gfjUbGhqaeZm+2fTbx8xfw5infgQr1zMwemRczezX09OT9vR+5hVOhB/B8qpZ/wiW/o1rK38ECwg61/8WLCAMCA1wAKEBDiA0wAGEBjjgX3j3f59X8TUbAAAAAElFTkSuQmCC)
From the figure we see that,
![](data:image/png;base64,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)
Tan θ = √3
But, tan 60 = √3
θ = 60⁰
Question 26.If the ratio of the height of a tower and the length of its shadow is 1 : √3, then the angle of elevation of the sun has measure ………….
A. 30
B. 45
C. 60
D. 75
Answer:![](data:image/png;base64,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)
Let the height of tower be h and length of the shadow be a
Now, ![](data:image/png;base64,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)
From the figure we see that,
![](data:image/png;base64,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)
But ![](data:image/png;base64,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)
θ = 30⁰
Question 27.If the angles of elevation of a tower from two points distance a and b (a > b) from its foot on the same side of the tower have measure 30 and 60, then the height of the tower is ……….
A. ![](data:image/png;base64,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)
B. ![](data:image/png;base64,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)
C. ![](data:image/png;base64,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)
D. ![](data:image/png;base64,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)
Answer:Let the height of the tower be h.
![](data:image/png;base64,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)
From the figure we see that,
and ![](data:image/png;base64,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)
Now, ![](data:image/png;base64,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)
![](data:image/png;base64,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)
H2 = ab
H = √ab
Question 28.The tops of two poles of height 18 m and 12 m are connected by a wire. If the wire makes an angle of measure 30 with horizontal, then the length of the wire is
A. 12 m
B. 10 m
C. 8 m
D. 4 m
Answer:Let the length of the wire be l.
![](data:image/png;base64,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)
From the figure we see that,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
L = 12 m
Question 29.The angle of elevation of the top of the building A from the base of building B has measure 50. The angle of elevation of the top of the building B from the base of building A has measure 70. Then, ………….
A. building A is taller than building B.
B. Building B is taller than building A.
C. Building A and building B are equally tall.
D. The relation about the heights of A and B cannot be determined.
Answer:Let the height of the building B be b and the height of the building A be a and the distance between the two building be x.
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)
From the figure we see that,
and ![](data:image/png;base64,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)
and ![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
b>a
Height of building B> Height of building A
Question 30.If the angle of elevation of the top of a tower of a distance 400 m from its foot has measure 30, then the height of the tower is ……..
A. 200√2
B. ![](data:image/png;base64,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)
C. ![](data:image/png;base64,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)
D. ![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
From the figure we see that,
![](data:image/png;base64,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)
H = 400 tan 30
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 31.The angle of depression of a ship from the top of a tower 30 m height has measure 60. Then, the distance of the ship from the base of the tower is ………..
A. 10
B. 30
C. 10√3
D. 30√3
Answer:![](data:image/png;base64,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)
Let the distance of the ship from the base of the tower be h.
From the figure we see that,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
h = 10√3
Question 32.When the length of the shadow of the pole is equal to the height of the pole, then the angle of elevation of the source of light has measure
A. 45
B. 30
C. 60
D. 75
Answer:![](data:image/png;base64,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)
Let the length of the pole be h and so the length of the shadow become h.
Suppose the angle of elevation of the sun is θ.
From the figure we see that,
![](data:image/png;base64,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)
θ = 45⁰
Question 33.From the top of a building h metre high, the angle of depression of an object on the ground has measure θ. The distance (in metres) of the object from the foot of the building is
A. h sinθ
B. h tanθ
C. h cotθ
D. h cosθ
Answer:![](data:image/png;base64,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)
Let the distance of the object from the foot of the building be l.
From the figure we see that,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
The distance of a point from the building l = h cot θ
Question 34.As observed from the top of the light house the angle of depression of the two ships P and Q anchored in the sea to the same side are found to have measure 35 and 50 respectively. Then from the light house....
A. P and Q are at equal distance.
B. The distance of Q is more then P.
C. The distance of P is more than Q.
D. The relation about the distance of P and Q cannot be determined.
Answer:![](data:image/png;base64,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)
From the figure we see that,
The distance of P from the lighthouse is more than the distance of Q from the lighthouse.
Question 35.Two poles are x metres apart and the height of one is double than that of the other. If from the mid – point of the line joining their feet, an observer finds the angle of elevation of their tops to be complementary, then the height of the shorter pole is
A. ![](data:image/png;base64,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)
B. ![](data:image/png;base64,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)
C. ![](data:image/png;base64,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)
D. ![](data:image/png;base64,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)
Answer:Let the height of the poles be h and 2h respectively.
Let the angles of elevation of the top of the poles from the midpoint M of the line joining the feet of the poles be α and ß.
Also, given that they are complementary angles, α + ß = 90⁰
![](data:image/png;base64,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)
From the figure we see that,
and ![](data:image/png;base64,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)
and ![](data:image/png;base64,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)
Now,
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tan (90 – α) = 2 tan α
cot α = 2 tan α
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Now,
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The height of the shorter pole is
.
A pole stands vertically on the ground. If the angle of elevation of the top of the pole from a point 90 m away from the pole has measure 30, find the height of the pole.
Answer:
Suppose AB represents the pole. C is a point 90m away from the pole.
AB = Height of the pole
BC = 90m
∠B is a right angle in ∆ABC and ∠C = 30⁰
In ∆ABC,
Thus, the height of the pole is 51.9 m.
Question 2.
A string of a kite is 100 m long and it makes an angle of measure 60 with the horizontal. Find the height of the kite, assuming that there is no slack in the string.
Answer:
Let PR be the string of a kite P and QR be the horizontal direction.
PR = 100 m
∠PQR = 90⁰
∠PRQ = 60⁰
PQ = Height of the kite
In ∆PQR,
PQ = 50√3
= 50 × 1.73
= 86.5 m
The height of a kite is 86.5 m.
Question 3.
A circus artist is climbing from the ground along a rope stretched from the top of a vertical pole and tied at the ground. The height of pole is 10 m and the angle made by the rope with ground level has measure 30. Calculate the distance covered by the artist in climbing to the top of the pole.
Answer:
Let PQ be the pole, whose height is 10 m and PR be the length of a rope stretched from the top of a vertical pole. The artist is moving from R to P.
The angle made by the rope with ground level has measure 30⁰.
∠PRQ = 30⁰
In ∆PQR,
PR = 10 × 2
= 20 m
The distance covered by the artist in climbing to the top of the pole is 20m.
Question 4.
A tree breaks due to a storm and the broken part bends such that the top of the tree touches the ground making an angle having measure 30 with the ground. The distance from the foot of the tree to the point where the top touches the ground is 30 m. Find the height of the tree.
Answer:
Suppose AC is the tree broken at point B such that the broken part CB takes the position BD and touches the ground at D.
AD = 30 m
∠ADB = 30⁰
In ∆DAB,
AB = 10√3
Now,
BD = 20√3
So, height of the tree AC,
= AB + BC
= AB + BD
= 10√3 + 20√3
= 30√3
= 30 × 1.73
= 51.9 m
The height of the tree is 51.9 m.
Question 5.
An electrician has to repair an electric fault on the pole of height 5 m. He needs to reach a point 2 m below the top of the pole to undertake the repair work. What should be the length of the ladder that he should use, which when inclined at an angle of measure 60 to the horizontal would enable him to reach the required position.
Answer:
Let PR represent a polle oof length 5 m.
Q is a point 2 m below the top of the pole P to undertake the repair work.
PQ = 2 m
QR = 3 m
QS = Length of the ladder
∠QSR = 60⁰
In ∆QRS,
QS = 2√3
= 2 × 1.73
= 3.46 m
The length of ladder is 3.46 m.
Question 6.
As observed from a fixed point on the bank of a river, the angle of elevation of a temple on the opposite bank has measure 30. If the height of the temple is 20 m, find the width of the river.
Answer:
Let PQ represent the temple and P is the top of the temple.
PQ = 20 m
R is a fixed point on the bank of a river from a temple on the opposite bank and QR is the width of the river.
∠PRQ = 30⁰
In ∆PQR,
QR = 20√3
= 20 × 1.73
= 34.6 m
The width of the river is 34.6 m.
Question 7.
As observed from the top of a hill 200 m high, the angles of depression of two vehicles situated on the same side of the hill are found to have measure 30 and 60 respectively. Find the distance between the two vehicles.
Answer:
Let PQ be the hill with height = 200 m
R and S are two vehicles situated on the same side of the hill.
The angles of depression of vehicles R and S from P are 60⁰ and 30⁰ respectively, so
∠PRQ = ∠XPR = 60⁰
∠PSQ = ∠XPS = 30⁰
SR = Distance between the two vehicles
In ∆PQR,
In ∆PQS,
QS = 200√3
Distance between the two vehicles situated on the same side of the hill = SR
= QS – QR
= 230.6
The distance between two vehicles is 230.36 m.
Question 8.
A person standing on the bank of a river, observes that the angle subtended by a tree on the opposite bank has measure 60. When he retreats 20 m from the bank, he finds the angle to have measure 30. Find the height of the tree and the breadth of the river.
Answer:
Let PM be the tree. OM represent the width of the river.
So, ∠PMO = 90⁰ and OA = 20 m
Let OM = Breadth of the river = x and
PM = Height of a tree = h
AM = OM + OA = x + 20
In ∆PMO,
H = √3x …………(1)
In ∆PAM,
……………(2)
From (1) and (2) we get,
X + 20 = √3x × √3
X + 20 = 3x
3x – x = 20
2x = 20
X = 10
Now, h = √3x
= 1.73 × 10
= 17.3
The breadth of the river = OM = x = 10 m and
The height of the tree = PM = h = 17.3 m
Question 9.
The shadow of a tower is 27 m, when the angle of elevation of the sun has measure 30. When the angle of elevation of the sun has measure 60, find the length of the shadow of the tower.
Answer:
Let AB be the tower and CB its shadow when the angle of elevation of the sun is 30⁰.
∠ACB = 30⁰
∠B = 90⁰
CB = 27 m
DB is the shadow of the tower when the angle of elevation of the sun is 60⁰.
In ∆ACB,
In ∆ADB,
The length of the shadow of the tower is 9 m.
Question 10.
From a point at the height 100 m above the sea level, the angles of depression of a ship in the sea is found to have measure 30. After some time the angle of depression of the ship has measure 45. Find the distance travelled by the ship during that time interval.
Answer:
Let the ship travel from A to Bin given time. So, the distance travelled by ship is AB.
Suppose, the observation point is at O.
OC = 100 m
The angle of depressions of A and B from O are 30⁰ and 45⁰ respectively.
∠OAC = ∠XOA = 30⁰
∠OBC = ∠XOB = 45⁰
In ∆OCB,
BC = 100
In ∆OCA,
100 + AB = 173
AB = 173 – 100
= 73 m
The distance travelled by ship during the given time is 73 m.
Question 11.
From the top of a 300 m high light – house, the angles of depression of the top and foot of a tower have measure 30 and 60. Find the height of the tower.
Answer:
Let AC be the lighthouse and ED be the tower.
Height of lighthouse = AC = 300 m
Let ED = h
Let EB be the perpendicular from E to AC.
The angles of depression of the top E and bottom D of the tower ED measures 30⁰ and 60⁰ respectively from A.
∠AEB = 30⁰
∠ADC = 60⁰
In ∆ADC,
Now, In ∆AEB,
AB = 100 m
Height of the tower ED = BC
= AC – AB
= 300 – 100
= 200 m
The height of the tower is 200m.
Question 12.
As observed from a point 60 m above a lake, the angle of elevation of an advertising balloon has measure 30 and from the same point the angle of depression of the image of the balloon in the lake has measure 60. Calculate the height of the balloon above the lake.
Answer:
Let BE be the surface of the lake.
A is a point 60 m above a lake.
F is the image of balloon C in the lake.
Horizontal line AD intersects CE in D.
∠CAD = 30⁰, ∠FAD = 60⁰, AB = 60 m
Let CE = h, BE = l
Then CD = h – 60, DF = h + 60
In ∆ADC,
L = √3(h – 60)……….(1)
In ∆ADF,
√3l = h + 60…………(2)
From equation (1) and (2),
√3[√3(h – 60)] = h + 60
3(h – 60) = h + 60
3h – 180 = h + 60
2h = 240
H = 120 m
The height of balloon above the lake is 120 m.
Question 13.
Watching from a window 40 m high of a multi – storeyed building, the angle of elevation of the top of a tower is found to have measure 45. The angle of elevation of the top of the same tower from the bottom of the building is found to have measure 60. Find the height of the tower.
Answer:
Let CD be the window, AB be the tower and D the point of observation.
CD = 40 m
Let the height of the tower = AB = h
Horizontal line DE intersects AB in E.
BE = CD = 40 m
AE = AB – BE = (h – 40)
∠AED = ∠ABC = 90⁰
Now, the angle of elevation of A from D is 45⁰ and the angle of elevation of A from C is 60⁰.
∠ADE = 45⁰, ∠ACB = 60⁰
In ∆AED and in ∆AEC,
DE = h – 40 = BC ………..(1)
H = (h – 40)√3
H = √3h – 40√3
H(√3 – 1) = 40√3
= 60 + 20(1.73)
= 60 + 34.6
= 94.6 m
The height of tower is 94.6 m.
Question 14.
Two pillars of equal height stand on either side of a road, which is 100 m wide. The angles of elevation of the top of the pillars have measure 60 and 30 at a point on the road between the pillars. Find the position of the point from the nearest end of a pillars and the height of pillars.
Answer:
Let AB and DE be two pillars of equal height.
AB = DE
The angle of elevation of A and E from C are respectively 60⁰ and 30⁰ respectively.
∠ACB = 60⁰, ∠EDC = 30⁰ and BD = 100 m
Let BC = x
CD = BD – BC = 100 – BC = (100 – x)
In ∆ABC,
… …. (1)
In ∆EDC,
(AB = DE)
100 – x = √3AB
100√3 – AB = 3AB
4AB = 100√3
AB = 25√3
= 25 × 1.73
= 43.25 m
The height of the pillar is 43.25 m.
From equation(1),
= 25
The distance of the point from the nearest end of the pillars is 25 m and the height of each pillar is 43.25 m.
Question 15.
The angles of elevation of the top of a tower from two points at distance a and b metres from the base and in the same straight line with it are complementary. Prove that the height of the tower is metres.
Answer:
AB is a tower. D and Care two points on the same side of a tower, BD = a and BC = b.
∠ADB and ∠ACB are the complementary angles.
If ∠ADB = x, then ∠ACB = 90 – x
In ∆ADB,
………… (1)
In ∆ABC,
…………....(2)
Multiplying (1) and (2),
(AB)2 = ab
AB = √ab
Height of tower = AB = √ab
Hence proved.
Question 16.
A man on the top of a vertical tower observes a car moving at a uniform speed coming directly towards it. If it takes 12 minutes for the angle of depression to change its measure from 30 to 45, how soon after this, will the car reach the tower?
Answer:
Let AB be the tower with height of tower AB = h
At C the angle of depression of car measures 30 and 12 minutes later it reaches D where angle of depression is 45.
Let CD = x, D = y
Here, AB = h, ∠ACB = ∠XAC = 30⁰
∠ADB = ∠XAD = 45⁰
In ∆ACB,
x + y = √3h ……(1)
In ∆ABD,
H = y ………(2)
From equation 1 and 2,
x + y = √3y
x = (√3 – 1)y
The distance covered by car in 12 minutes is CD = x
So, time taken to cover distance x is 12 minutes.
So, y = Time taken to cover distance DB
= 6 × 2.73
= 16.38 minutes
The time taken by car to reach the tower is 16.38 minutes.
Question 17.
If the angle of elevation of a cloud from a point h metres above a lake has measure a and the angle of depression of its reflection in the lake has measure β, prove that the height of the h(tani3 + tana) cloud is .
Answer:
Let AB be the surface of the lake. E is the point above h metre from A.
AE = h
Let height of the cloud BD = l
Let F be the reflection of kite C.
Horizontal line EC intersects BD in C.
BF = l
∠DEC = α, ∠CEF = ß
Here, AE = BC = h
CD = BD – BC = l – h and
CF = BF + BC = l + h
In ∆ECD,
……(1)
In ∆ECF,
…….(2)
From results (1) and (2),
Using componendo – dividendo,
The height of the cloud from the surface of the lake is m.
Hence proved.
Question 18.
From the top of a building , 60 m high, the angles of depression of the top and bottom at a vertical lamp post
are observed to have measure 30 and 60 respectively. Find,
(1) the horizontal distance between building and lamp post.
(2) the height of the lamp post.
(3) the difference between the heights of the building and the lamp post.
Answer:
Let AB be the building and CD be the lamppost.
The height of the building AB = 60 m
Horizontal line DE intersects AB in E.
Let BE = CD = x
AE = AB – BE = (60 – x) m
∠AED = ∠ABC = 90⁰
Now, the angle of depression of the top D and then bottom C of the post CD are 30⁰ and 60⁰ respectively from A.
Then, ∠ADE = ∠XAD = 30⁰ and
∠ACB = ∠XAC = 60⁰
In ∆ADE,
DE = √3(60 – x) ………(1)
In ∆ABC,
…………..(2)
Now, BC = DE
From (1) and (2),
√3(60 – x) = 20√3
60 – x = 20
X = 40
1) The horizontal distance between the building and the lamppost
= BC
= √3(60 – x)
= √3(60 – 40)
= 20√3
= 20 × 1.73
= 34.6
2) The height of the lamppost
= CD
= x
= 40 m
3) The difference between the heights of the building and the lamppost
= AB – BE
= 60 – x
= 60 – 40
= 20 m
Question 19.
A bridge across a valley is h metres long. There is a temple in the valley directly below the bridge. The angles of depression of the top of the temple from the two ends of the bridge have measures α and β. Prove that the height of the bridge above the top of the temple is
Answer:
Let AD be the bridge and E be the top of the temple.
The perpendicular from E on AD is EF.
Thus, EF represents the height from the top of the temple to the bridge.
Let EF = x and DF = y
AF = h – y
In ∆ABE,
………(1)
In ∆DCE,
………..(2)
From (1) and (2),
h tan α tan ß – x tan ß = x tan α
h tan α tan ß = x(tan α + tan ß)
The height of the bridge above the top of the temple is .
Question 20.
At a point on level ground, the angle of elevation of a vertical tower is found to be such that its tangent is . On walking 192 metres towards the tower, the tangent of the angle is found to be
. Find the height of the tower.
Answer:
Let AB be the tower.
The angle of elevation of tower from D is α and on walking 192 metres towards the tower from D to B, the angle of elevation of tower from C is ß.
CD = 192 m
,
Let BC = x, AB = h
BD = BC + CD = x + 192
∠ADB = α ∠ACB = ß
In ∆ABC,
4h = 3x
…..equation (1)
In ∆ABD,
12h = 5x + 960
36h = 20h + 2880
16h = 2880
H = 180
The height of the tower = AB = h = 180 m.
Question 21.
A statue 1.46 m tall, stands on the top of a pedestal. From the point on the ground the angle of elevation of the top of the statue has measure 60 and from the same point, the angle of elevation of the top of the pedestal has measure 45. Find the height of the pedestal.
Answer:
Let AB be the pedestal and AB = x
BC is a statue and BC = 1.46 m
The angle of elevation of the top of the statue C from D is 60⁰ and from the same point the angle of elevation of the top of the pedestal B is 45⁰.
In ∆BAD,
AD = x
In ∆CAD,
√3x = x + 1.46
(√3 – 1)x = 1.46
(1.73 – 1)x = 1.46
0.73x = 1.46
X = 2
The height of the pedestal is = AB = x = 2 m.
Question 22.
On walking ……….. metres on a hill making an angle of measure 30 with the ground, one can reach the height of 'a' metres from the ground.
A.
B.
C. 2a
D.
Answer:
Suppose on walking h metres, one can reach the height of “a” metres from the ground.
H = 2a
Question 23.
The angle of elevation of the top of the tower from a point P on the ground has measure 45. The distance of the tower from the point P is a and height of the tower is b. Then, ……….
A. a > b
B. a ∠ b
C. a = b
D. a = 2b
Answer:
From the figure we see that,
A = b
Question 24.
A 3 m long ladder leans on the wall such that its lower end remains 1.5 m away from the base of the wall. Then, the ladder makes an angle of measure ……… with the ground.
A. 30
B. 45
C. 60
D. 20
Answer:
From the figure we see that,
But,
θ = 60⁰
Question 25.
A tower is 50√3 m high. The angle of elevation of its top from a point 50 m away from its foot has measure
A. 45
B. 60
C. 30
D. 15
Answer:
From the figure we see that,
Tan θ = √3
But, tan 60 = √3
θ = 60⁰
Question 26.
If the ratio of the height of a tower and the length of its shadow is 1 : √3, then the angle of elevation of the sun has measure ………….
A. 30
B. 45
C. 60
D. 75
Answer:
Let the height of tower be h and length of the shadow be a
Now,
From the figure we see that,
But
θ = 30⁰
Question 27.
If the angles of elevation of a tower from two points distance a and b (a > b) from its foot on the same side of the tower have measure 30 and 60, then the height of the tower is ……….
A.
B.
C.
D.
Answer:
Let the height of the tower be h.
From the figure we see that,
and
Now,
H2 = ab
H = √ab
Question 28.
The tops of two poles of height 18 m and 12 m are connected by a wire. If the wire makes an angle of measure 30 with horizontal, then the length of the wire is
A. 12 m
B. 10 m
C. 8 m
D. 4 m
Answer:
Let the length of the wire be l.
From the figure we see that,
L = 12 m
Question 29.
The angle of elevation of the top of the building A from the base of building B has measure 50. The angle of elevation of the top of the building B from the base of building A has measure 70. Then, ………….
A. building A is taller than building B.
B. Building B is taller than building A.
C. Building A and building B are equally tall.
D. The relation about the heights of A and B cannot be determined.
Answer:
Let the height of the building B be b and the height of the building A be a and the distance between the two building be x.
From the figure we see that,
and
and
b>a
Height of building B> Height of building A
Question 30.
If the angle of elevation of the top of a tower of a distance 400 m from its foot has measure 30, then the height of the tower is ……..
A. 200√2
B.
C.
D.
Answer:
From the figure we see that,
H = 400 tan 30
Question 31.
The angle of depression of a ship from the top of a tower 30 m height has measure 60. Then, the distance of the ship from the base of the tower is ………..
A. 10
B. 30
C. 10√3
D. 30√3
Answer:
Let the distance of the ship from the base of the tower be h.
From the figure we see that,
h = 10√3
Question 32.
When the length of the shadow of the pole is equal to the height of the pole, then the angle of elevation of the source of light has measure
A. 45
B. 30
C. 60
D. 75
Answer:
Let the length of the pole be h and so the length of the shadow become h.
Suppose the angle of elevation of the sun is θ.
From the figure we see that,
θ = 45⁰
Question 33.
From the top of a building h metre high, the angle of depression of an object on the ground has measure θ. The distance (in metres) of the object from the foot of the building is
A. h sinθ
B. h tanθ
C. h cotθ
D. h cosθ
Answer:
Let the distance of the object from the foot of the building be l.
From the figure we see that,
The distance of a point from the building l = h cot θ
Question 34.
As observed from the top of the light house the angle of depression of the two ships P and Q anchored in the sea to the same side are found to have measure 35 and 50 respectively. Then from the light house....
A. P and Q are at equal distance.
B. The distance of Q is more then P.
C. The distance of P is more than Q.
D. The relation about the distance of P and Q cannot be determined.
Answer:
From the figure we see that,
The distance of P from the lighthouse is more than the distance of Q from the lighthouse.
Question 35.
Two poles are x metres apart and the height of one is double than that of the other. If from the mid – point of the line joining their feet, an observer finds the angle of elevation of their tops to be complementary, then the height of the shorter pole is
A.
B.
C.
D.
Answer:
Let the height of the poles be h and 2h respectively.
Let the angles of elevation of the top of the poles from the midpoint M of the line joining the feet of the poles be α and ß.
Also, given that they are complementary angles, α + ß = 90⁰
From the figure we see that,
and
and
Now,
tan (90 – α) = 2 tan α
cot α = 2 tan α
Now,
The height of the shorter pole is .