Class 10th Mathematics CBSE Solution
Exercise 9.1- A circus artist is climbing a 20 m long rope, which is tightly stretched and…
- A tree breaks due to storm and the broken part bends so that the top of the tree…
- A contractor plans to install two slides for the children to play in a park. For…
- The angle of elevation of the top of a tower from a point on the ground, which…
- A kite is flying at a height of 60 m above the ground. The string attached to…
- A 1.5 m tall boy is standing at some distance from a 30 m tall building. The…
- From a point on the ground, the angles of elevation of the bottom and the top of…
- A statue, 1.6 m tall, stands on the top of a pedestal. From a point on the…
- The angle of elevation of the top of a building from the foot of the tower is 30…
- Two poles of equal heights are standing opposite each other on either side of…
- A TV tower stands vertically on a bank of a canal. From a point on the other…
- From the top of a 7 m high building, the angle of elevation of the top of a…
- As observed from the top of a 75 m high lighthouse from the sea-level, the…
- A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at…
- A straight highway leads to the foot of a tower. A man standing at the top of…
- The angles of elevation of the top of a tower from two points at a distance of…
- A circus artist is climbing a 20 m long rope, which is tightly stretched and…
- A tree breaks due to storm and the broken part bends so that the top of the tree…
- A contractor plans to install two slides for the children to play in a park. For…
- The angle of elevation of the top of a tower from a point on the ground, which…
- A kite is flying at a height of 60 m above the ground. The string attached to…
- A 1.5 m tall boy is standing at some distance from a 30 m tall building. The…
- From a point on the ground, the angles of elevation of the bottom and the top of…
- A statue, 1.6 m tall, stands on the top of a pedestal. From a point on the…
- The angle of elevation of the top of a building from the foot of the tower is 30…
- Two poles of equal heights are standing opposite each other on either side of…
- A TV tower stands vertically on a bank of a canal. From a point on the other…
- From the top of a 7 m high building, the angle of elevation of the top of a…
- As observed from the top of a 75 m high lighthouse from the sea-level, the…
- A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at…
- A straight highway leads to the foot of a tower. A man standing at the top of…
- The angles of elevation of the top of a tower from two points at a distance of…
Exercise 9.1
Question 1.A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is 30° (see Fig. 9.11)
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)
In this figure; AC is the rope which is 20 m long and we have to find AB (height of the pole).
In Δ ABC;
We know,
![](data:image/png;base64,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)
where p = perpendicular and h = hypotenuse
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Hence, Height of the pole, AB = 10 m
Question 2.A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30° with it. The distance between the foot of the tree to the point where the top touches the ground is 8 m. Find the height of the tree
Answer:
Let BAC be the tree.
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ZN137+/6rj5FtKL1qitIIyFVRtTvTQ5hQBDQAAgMcWGulXT+MRdTceUaDtmsxoRA5ncqZmcn4qAAAAPBWx6SkNtV5Qx6m3NN5xQ2YsKqcnVb78EmWUVCTd8g2JgAYAAMAjsCxT45231HP2sPovf6DIZECG06m81TVyOF0aam2Ww+NN9DCfCAIaAAAAtkSDE+q9cEJdp9/R1ECnLNOc3TC47QvKX12jwavnNHT9gmRZiR7qE0FAAwAA4KHEoxGNt7eq7fibGr11WdHpoNypacpfU6vS+n3y5ZXMrntO0nD+CAENAACAzxUc6FZv8/vqaTys6cCQDBnKemaVSmr3KHflejm9qZJlybJMJXc+E9AAAAD4DLHpoAavNqmr4aACba0yYxF50rNUXP28CtfWy5dfIss0k37W+VcR0AAAAPgEyzQ11d+hjpNvaeByg8ITY3K43cpdsUFlW16Sv3y5nC7PbDwvMgQ0AAAAPiY8MaqByw1qf/9NhUb6ZcViSssvUenmvcp/rk5uX4ak2ZM4FiMCGgAAAJJmbxIcvXlJnR+8q+HrzYrNTMvtS1f++hqV1OxWetESyTAW1XKNByGgAQAAoOBQj3oa31PfhRMKDfdLhpRZvlylm19U7op1cqX4FuVyjQchoAEAABaxeHhaQ9fOq/3Efo133lQ8GpYnLVMltbtVtGGbUrILJIl4/hUENAAAwCJkmaYme+6q88w76r94StHgpBwut/JWVat868vyl1bK4XLJWuTLNR6EgAYAAFhkZsZHNHDpjDrPvKPgQJcs01RaQZmKa55X/nN18qRlSrKI509BQAMAACwSZiyqkVuX1PXBQY3caFFsOihnSqoKqupVvHGHMkqXzT5IOH8mAhoAACDZWZamxwbV1XBIvU3vaXpsSIZhKKOkQkt2/KayK9bIlcomwYdFQAMAACSxaGhKwzcuqP34m5rovqN4NKwUf66KNmxTcc1uef3ZkmEQzzYQ0AAAAEkq0H5d3Y1HNHDxtCLBcTlcHuU/W6uS2j3KXLpSDqdbksWSDZsIaAAAgCQTnhhV34WT6m48oqnedlmWqdScIpXV71Pe6o3y+nNlmXFJhPOjIKABAACShBmNKNDeqrb3/1ejNy8pOj0ld2qa8tfUqXTzXqXll8pwOO7FMx4VAQ0AAJAEgoPd6j1/XF0fHFRkckySlLl0lcrrX1LO8rVyeLySxdF0c4GABgAAWMBiMyENfnhWXQ0HNdbWKiselTczV0Xrt6lw/XalZufPPkg4zxkCGgAAYAGyTFMT3bfVeeYdDV5pVGRiTIbLpdyVG1W2+UVlLlkph8sty+J0jblGQAMAACwwkcmA+lpOqfP0AQUHuu9tEixU+daXlfdsjdxp/nuHaxDPTwIBDQAAsECY0YhG71xR56kDGr5xQbHwtNyp6cpfU6vSzS8qLa9EcjhYrvGEEdAAAAALQHCgSz3nj6u36aimA4MyDIeynlmt0k0vKKdyrZwpqbPhTDw/cQQ0AADAPBabCWngw7PqbjioQPt1mdGIPBmZKq7ZpcK1W+XLK5JlEs5PEwENAAAwD1lmXJO9Heo89Uv1Xz6jyOS4nB6vclesV/n2L8pfWiGHy8MV3AlAQAMAAMwzM4FhDVz+QB0nf6nQcK8s01RaYZlKa/eoYG29XCk+SWwSTBQCGgAAYJ6wzLiGWpvVffawhq83KzYzLXdqmgqq6lRc/bzSC5dIhpHoYS56BDQAAECiWZaCw33qPntIfRdOaHpkQIZhyF+2TEu2/YayKtbInZrOFdzzBAENAACQQLHpoIZam9VxYr/GO28qHo0oJTNHRRt3qrh6p7z+HMkwiOd5hIAGAABIAMsyNd5xU92NR9R34YRi00E5XG7lP1ujsvp98pcvl+F0cTTdPERAAwAAPGXhiVH1Nr+vnsb3NNnXLlmW0gpKVVK7W/nP1sqdnkk4z2MENAAAwFNixqIauXVZnacPaPTWZUVDU3Kl+lTwXJ1KavcovWiJDMOQRTjPawQ0AADAUxAa6lVP03vqPntYM4FhGU6X/GWVWrrjN5W1bI1cnhRZlkU8LwAENAAAwBMUnZ7S0NVz6jx9QIGOm7JiUXkzc1W0YZuKq3fJ68+WJMJ5ASGgAQAAnpBAe6u6Gw5r4PIHigTH5XB5lLemViWbXpC/fLkcLjfrnBcgAhoAAGCOhSfG1Hv+uHqajmiyr0OyLKXmFqm8/iXlrq6WNyN79lg64nlBIqABAADmiBmNaOzuVbWffEsjN1oUmwnJk+ZX3upqlW15Wb7cIsnh4EznBY6ABgAAmANT/Z3qa35fXWcPKTwxJsMwlPXMapVuflG5K9bPLteQmHVOAgQ0AADAY4iHZ9R/8ZS6G49orK313ibBHBVX71Th2q1KySkgmpMMAQ0AAPAILDOuie476jh1QENXmxSeGJPT41XOyg0q3/YFZZQuk9PtkWWaiR4q5hgBDQAAYFN4fET9F8+o8/QBTQ1237tJsEyldS+ooGqzXKlpkiXiOUkR0AAAAA/JjEU1cqNFXQ2HNNTaLDM6I1dqugrWbFLJpj1KKyibfZAlG0mNgAYAAPg8lqXgUI+6zx5W34UTCo0MyOF0KnPJKpXVv6jsZc/J5U3lMpRFgoAGAAD4DLGZkAYuN6jrg3c03nlL8Uh4dpPgxp0q2rBdqdn5ssRNgosJAQ0AAPAAlmlqouu2uhreVX/LKUWCk3KlpCpv1UYt2fFFZZRUyHC6COdFiIAGAAD4NTOBYfW3nFJXw0EFB7pkWZbSi5aopGaXCtbWy5Xim32QeF6UCGgAAIB7LDOu4dZmdX5wUCM3Z28SdKemq6Bqs0pqds1uEnQ4COdFjoAGAACwLAWHetXVcFD9F05qenRAhtOpzPLlWrLti8p65lm5Un2zx9IRz4seAQ0AABa1aGhKQ9fOqfP02wq0X5cZiyg1u0CF67aqpHa3PBlZkmFwpjPuI6ABAMCiZFmWAu2t6ml8T30tJxWbDsrh9ih/VZ1K6/Yqs3yFDIfjo4cTPVzMIwQ0AABYdCJTAXWfPaLe88c12dsmSUrLL1Fp3V7lPVsjT1qmLIsZZzwYAQ0AABYNMxrRyO0P1XFiv8buXFF0ekpuX4byn61Vaf0+peUVy3A4iWd8JgIaAAAsCsGBLvWcO6aexiOaCQzLcLqU9cxqldW/pJzla+VweyTLIp7xuQhoAACQ1GIzIfVfPK2exiMaa2+VFY/Jm5Wnog3bVLxhp7xZubNrnFnnjIdEQAMAgKRkmabGu26p8/TbGrrSqPBUQE63V7mra1RW/5IySivkdLm5SRC2EdAAACDphMdH1Xv+uLobD2tqoEsyTaUVlKqs7kXlPVsrT7pflmkRz3gkBDQAAEgaZjSikVuX1XXmHQ1fv6BYeFqejEzlrdyosi0vyZdXJBkOznTGYyGgAQBAUpjq71RP03vqPX98dpOgw6nsZWtUsmmPclesl8PlkcRaZzw+AhoAACxo8UhYfS0n1N1wWIGOGzJjEaX4c1Vc87wK129TSlbe7IOEM+YIAQ0AABYkKx7XeNdtdZ4+oKGrTQpPBuTypihn1UYt2f6bSi9eKqfbw3INzDkCGgAALDgzgWH1t5xS19lDmurvlExTGcVLVVyzSwVr6+VK8c2e6Uw84wkgoAEAwIJhxqIabm1Wd+NhDbU2y4xG5E5NU/5zm1VSu0tpBWWzD7JcA08QAQ0AAOY9y7I0PdKvztMH1H/xtEIj/XI4XcpcskLlW15WVsUaubyp3CKIp4KABgAA81p0ekqDHzaq89QBTfTcUTwyo5TsfBWt36bi6l3y+rMlwyCe8dQQ0AAAYF6yLEvj7dfVffaw+i+eViQ0IZfXp/w1m1RW/5L85ZUyDMdHDyd6uFhECGgAADDvhMdH75/pPNnfLklKL1qiktrdKlhTJ7cvnVsEkTAENAAAmDfMWFQjNy+q49QBjd6+rNh0UG5fhgqq6lRat1epuUUyHE7iGQlFQAMAgHkhONClroZD6rtwQjNjQzIcTmU9s1plW15W9rLn5PKkzK5zJp6RYAQ0AABIqNlNgmfV1XBIgfZWmdGofLmFKli7RcU1z8ubkSPJYpMg5g0CGgAAJIRlmgq0X1d3w0ENfNigaHBSTo9XeVUbVbrpBfmXrLy3SZAZZ8wvBDQAAHjqIlPj6m44pJ7zx2ZvErRMpRWUqnTzi8p7tlae+5sEiWfMPwQ0AAB4auKRsEZvXVbHybc0eueKYtNBeTKylLd6o8q3vKyUnAI52CSIeY6ABgAAT8VUf6d6mo6qt/m4ZkYHZTidyl5epdLaPcpZuV4O52yWEM+Y7whoAADwRMVmQuprOamexvcUaG+VZZryZuWqeOPzKly/ValZeUQzFhQCGgAAPBFmPKbJnrtqP7Ffw9fOKzw5Jqc3Vbkrq1S+9QvKKH5GDpeb0zWw4BDQAABgzs0EhtXb/L66zx5SaLBXVjymjOJnVFyzSwVVm+VKTZMsEc9YkAhoAAAwZ8xYVMPXm9V99rCGW5sVC8/I689S3qoalda9IF9+yeyDLNnAAkZAAwCAx2dZCg71qPPMO+q/eFrTo4NyOJ3KXrZGpXUvKGf5OjndHtY6IykQ0AAA4LHEZkIauHRGnWfe0UTXbcVjEaVk5qm4eqeKNu6UNyNLMgziGUmDgAYAAI/EMk2Nd9xQx+m3NXS1SZGpcbm8qcpfU6vyLS8ro6RChtM1u1yDeEYSIaABAIBtM4ER9Z4/pt7zxzTZ1yGZpvyly1S0ccevbBIknJGcCGgAAPDQzFhUw63N6vrgXQ3fvCgzEpbbl66Cqs0qrtmttIKy2QcJZyQxAhoAAHwuyzQ1PTqgjpNvqf/SGU2PDsjhdClz6SqVb31Z2RVr5PSkcCwdFgUCGgAAfKZoaFIDH55V5+m3Ndl9R/FoWKm5RSpcu0UltbvlSc+8t0mQeMbiQEADAIAHsyyNtbWqu+GQBq403N8kWLh6i0pq9yhzyQrJMO4/CywWBDQAAPiE8MSYus8eUm/z+5rq65AkpRcuUWndC8p7tlaetAxZJjPOWJwIaAAAcF88MqPR2x+q/cR+jd29qth0UJ70TOWvqVVZ/UtKyS6Q4XAQz1jUCGgAACBJmurvVHfDIfW1nNRMYFiGYSi7skqlm/YoZ/k6OdwejqYDREADALDoxaaD6r94Wt1N7ynQ1iozHpUvt0iF67aqaMMOeTNzCGfgVxDQAAAsUpYZ13jnLXWcfEtDrecVmRyXy5uivNXVKq17Qf7yFTIcDsIZ+DUENAAAi1B4Ykw9jUfU3XhEwaEeyTKVXjS7STD/uTq5UnySJeIZeAACGgCARSQeDWvkxkV1njqg0TtXFJsJypuRpbxna1Ra96J8uUUSs87AZyKgAQBYJKb6u9TV8K4GLn2g6ZF+GQ6HclesV3H188pZwSZB4GER0AAAJLnYTEh9LSfV3XBI4503ZcXj8mblqqR6lwrXb1VKZt7sLYKEM/BQCGgAAJKUGYtqsqdN7e+/qaHrzYpMBuTypipnVbXKtr6kjOIKOZxOruAGbCKgAQBIQjNjQ+ptfl/dZw8rNNwrKx6Tv3SZijbuVMHaerm8qZIki1lnwDYCGgCAJGLGohpqPa/uDw5p5NZFxWam5cnIVGFVvYqqdyqtoIylGsBjIqABAEgClmUqNNyvjhP7NfBhg6ZHB+RwupS97FmVbd6n7GXPyelN4QpuYA4Q0AAALHDR4IQGrzSq49QvNdnTpng0rNScQhVt2K6Sml1yp/klwyCegTlCQAMAsEBZlqlAW6s6z7yroatNigQn5HJ7Vbh2i0o27ZG/bLkMh1MSR9MBc4mABgBgAQqPj6i78Yj6mk9osq9dsiz5SytUXL1L+Wtq5U5Nv3e6BuEMzDUCGgCABWT2JsFL6ji5X2N3r85uEkz3q6Bqs0pqdstXUCpJHE0HPEEENAAAC4BlmQoN9anz9AH1tZxSeHxYhsOp7GVrVFa/T9mVVXK43CzVAJ4CAhoAgHkuGprUwKUP1PXBu5rovqN4NCJfXpEK125RcfXz8mRkzT5IPANPBQENAMA8ZVmmxtuvq+PUAQ1fv6DwxJicHq+KNmxTcfXzyixfITkchDPwlBHQAADMQ+HxUXWfPaye80cVHOiWDEPpRUtUtvlF5a2uljstY/ZYOuIZeOoIaAAA5pFYeFpjt6+o/cT/auzuNcVmgvJkZKlgzSaVbn5RqTmFnOkMJBgBDQDAPDHV16Gus4fUf+GkZsZHJUm5K9aruPp55axYN7tJUGLWGUgwAhoAgASLzQTVd+GkuhuPaLzjpsxYVL7cQhVV71Th2q1KycplxhmYRwhoAAASxIzHNNF9R+3HfqHhmy2KTAbkSvEp79lqldW9qIzSZXI4XcQzMM8Q0AAAJMD02JD6mo+rq+GQpof7ZFmmMkqWqaR2lwqq6uX0eCVxIQowHxHQAAA8RWY0oqHWZnWdeUejd64oNhOavUlwbb1KqnfJl1+S6CEC+BwENAAAT4NlKTjYo45Tv9TglbOaHhmQ4XAod8U6lWzao+xlz8np9jLjDCwABDQAAE/YRzcJdp5+WxM9d2TGY0rNLlBx9fMqXL9VKf4cWWK5BrBQENAAADwhZiyqie476jixX0Ot5xUJTsjlSVH+s7Uq3bxX/tJKyeGQxbF0wIJCQAMA8ATMjA2p59wx9TS9p9BQrywzLn9ppYo37lB+1Wa5vKmzDxLPwIJDQAMAMIfMWFTDrc3qOHVAY21XFZsOypPmV9GG7SrasEO+gtLZBwlnYMEioAEAmAOWaSo01KuOU2+p/9IHmgkMyeFyK3vZcyrb8pKyn3lWTk8K65yBJEBAAwDwmCKTAQ1ebVLnqQOa7G1TPBqWL7dYheu3qaTmebnT/JIM4hlIEgQ0AACPyDJNBdpb1Xn6bQ1dO69oaFIOp1tFG3aoeONO+ZeskGEYHz2d6OECmCMENAAAjyA8MaquhkPqa35fU/2dkmUpo+QZlWx6QXmrq+X2pXMFN5CkCGgAAGyIh6c1cvtDtR//hQLt12dvEszIUsFzm1VSu1u+vGLJMIhnIIkR0AAAPATLshTs75yddb5wQuGJURkOh3KWr1Pppj3KWbFOhsP50cOJHi6AJ4iABgDgc0RDU+q/eEpdDYc02X1H8VhEvpxCFVXvVOHarfJm5hDNwCJCQAMA8CksM67xzltqO/4Ljd66rPDEmJwer4rWb1dJ7W5llFbI4XBxugawyBDQAAA8wOxNgkfVffawQsN9kqSMkmdUWrd3dpNgaposyyKegUWIgAYA4FfEZqY1evuyOk6+pbG71+5tEsxUQdW9TYK5JZIsWSzZABYtAhoAgHum+jrU9cG76r94WjPjIzIMQ7kr16u45nnlVK6Tw+1mrTMAAhoAgNh0UH0XT6nrzDua7GlTPBpRak6BSjbtUcFzm5WSlTt7LB3xDEAENABgETNjUU1031HbsTc0fKNF0eCkXCk+Fa6uVmn9PmUUPyOH08mZzgA+hoAGACxKoZF+9V84qa6zhzQ90i/LjMtfVqni6p0qqKqX0+OVJNY6A/gEAhoAsKiY0YiGWpvVefqAxu5eUzw8LXdquoqqd6hw/TalFZSxVAPAZyKgAQCLgmWaCg33qv3Efg1+eFbTY4NyOFzKXl6lss37lPXMajk9XpZrAPhcBDQAIOlFpsY1eKVRHSf2a7K/Q2YsKl9ukYo27lDRum3y+LMliXgG8FAIaABA0jJjUY133FTnmbc1ePWcYtOTcnq8KlhTp+LaXcosXzH7IEs2ANhAQAMAktJMYFjdjUfUe+6YgkM9kmkqo6RCJZv2fOwmQQCwi4AGACSVeCSs0VuXdPfYG5rovKXo9JTcaX4Vb9yhog075csrlgxO1wDw6AhoAEBysCxN9neo68y76ms5qfDEqJwuj3KWr53dJFjxrBxuz+xyDdoZwGMgoAEAC15kMqCBK2fVdeZdTfbcVTwWmd0kuGGHijZskycj+144U84AHh8BDQBYsCwzrkD7dXWc/KWGW5sVDU3K4fKoeMMOFVXvlL9suQyHg3AGMKcIaADAgjQzPqKes4fV3fSeQkO9kmUpvWSpyupfUu6K9XL70mePpSOeAcwxAhoAsKDEZkIavf2h2o69oUDHDcXDM/L6s1RQVa/iml3y5RZJhsGZzgCeGAIaALAwWJYmeu6qp+k99V2Y3SRoOBzKXblexTXPK3fFhtnlGveeBYAnhYAGAMx7semg+i6cVFfDu5rouSsrFlNKVp5K6/Yq/7lNSsnMk2Ux4wzg6SCgAQDzlhmLaqL7ttqOvqGRW5cVmRqX05uigvV1Kq17UelFS+RwuohnAE8VAQ0AmJdCI/3qaz6hroZ3NT06IFmSv2zZvZsEa+RK8UmWRTwDeOoIaADAvBKbCWnk5kV1nn5bY3evKh6ekTvNr6L121S0YbvSCkpnbxFknTOABCGgAQDzg2VpaqBLnacPqP/SGYUDIzIcDuUsX6eSuj3Krlgjp9vDFdzAE2DImPN3MyTJmMv3nT8IaABYBMbHxxUIBBSNRpWRkaGcnBy53e5ED+u+aGhSA5c+UPuJ/QoOdikejSg1u0CldXtVULVZ3oxsWbKIZ+AJMC1Toei0ovHonLyfYRiaikwpEo/KY8YkJd/fWwIaAJLY1NSUjh49qqNHj6qzs1PBYFB5eXnatm2bfvu3f1tFRUUJHZ8ZjynQdl2dp36podbzik5PyZ2Sprxna1VW96LSi5fKcDpZ5ww8IYYM3R5u01tX39FIaHROZqItSRltHcoavKV8Z0wrIiHlJPqDzjECGgCSVDAY1E9+8hMdPnxY+/bt07e+9S2lpaWppaVFP/vZzzQ4OKjvfe97yslJzLe20HCf+i6cUE/TewoN9cmyTPlLK1VSu0v5z9bKeW+TIGudgSfDkKFIPKrLfVfU2NmsaDwqa45mi4sDI3LMTMiYHNbEzESiP+qcI6ABIEmdOXNG+/fv1x//8R/ry1/+sox7axGXL1+urKwsff/739e6dev01a9+9f5rT4MZDWvoeos6TuxXoK1V8ciMXClpKqndpcL1W+XLL519kHAGnri4FdNkeEpxMyaXw6ktz9TJ5XA+8vtZkhwOp0IzTVJbn0zLkpmEt4IS0ACQhILBoI4cOaLKykrt3r37E4G8adMmfeELX1A8Hlc8HpfL9eS/HVimqeBgtzpO/VIDl85oZnxEDqdL2curVL7lZWUuWSmnx8sV3MBTZlqmTMtSitujfav2KDMl47GWLRsOh5p6R3TbOK9kXP8sEdAAkJRGRkZ06dIl7dmzRxkZGZ94PSsrS3/xF38hwzDkdD76bNPDCk+OafBKkzpO7tdUf6fMWEy+vGIVb9ypwnVb5MnInj3TmXgGEsYwDDkMQ16nV48TvobDIYccH/2vRH+sJ4KABoAkNDU1pfHxcfn9/k9dnvE0Zp3NeExjd6+q+4NDGrzWpNh0UE6PV4VV9Sqq3qnM8hWzD7JcA5gfLOvx10Fbuvceyfv3moAGgCTkcDjkcDgSeuxbeHxEXQ2H1HvuqIJDvZKk9MIlKtv6knJXrJfbl86MM7BInTt3Tn/3d3+nmZmZ+3/m8XhUU1OjV155RatXr36qezPsIqABIAllZ2errKxMo6OjMk1TDofjY69blqVAIKB4PK7s7Ow5XcYRm5nW6O3Lunv055rouq1YOCRPml9FG7arpGa3UrLzZRgG8QwsYv39/WpoaNCXv/xlFRYWSpJCoZCOHTumM2fO6G/+5m+0bt26RA/zUxHQAJCEsrKyVF1dratXr2p4ePgT5z2HQiH96Ec/ksfj0fe+970HrpN+FBPdd9TdeER9ze8rMhWQw+lW7or1Kt30grIq1sjhds/+ipglG8CiZhiG8vLy9K1vfUtVVVWSZn+wv3nzpr773e/q6NGjWrNmzVNZavYoHI//FgCA+cbr9Wrv3r0aHBzUG2+8oVAodP810zR15swZnThxQmVlZfL5fI/974tMBtR55h1d+T//qK7TbysyFVBqdoEq9nxVK3/zm8pdtUEOl4u1zgA+xul03l9y5nQ6VVhYqIyMDE1NTc3rH7TnZ9YDAB7b+vXr9c1vflP/9m//phs3bmjv3r3y+XxqamrSsWPHtHXrVn3pS196rOUbVjyuQMcNtZ/4X41cv6BIaFJOt1eF67ertHa30ksqZDgcLNcA8AmmaWpiYkKBQECSFI/HderUKTkcDtXX18/b2WeJgAaApOXxePS1r31NlZWVevvtt/Xv//7vmpqa0vLly/Wd73xHu3btUmZm5iO///TYoHqbjqmr4V3NjA3Jsiz5SypUtmV2k6ArJW32Cu55PIsEIDEMw1B/f79ee+01paSkSJoN6Gg0qm984xvatGkTmwgBAInhdru1efNm1dbWyjRNWZZ1/1elj/rNKTYT0siNFnWc+qXG7l5TPBqR15+tgqrNKql+Xqm5s+utLYtZZwAPZlmWsrKy9O1vf1vl5eWSpHA4rObmZh05ckR5eXn6+te/Lq/Xm+ihPlDSBfSvr5eZzz+9AMDT4nQ6H/+kDcu6v0mw/9JphcdHZTgcyl2xTiW1e5RTWSWDdc4AHpLP59MLL7ygNWvW3P+zV199VT/60Y/05ptvateuXaqsrEz0MB8oaQI6FArpxz/+sY4cOXJ/zYxhGCoqKtLevXv1xS9+UVlZWYkeJgAsSNHQlPovnlbn6QOa7G2XZcbk9eeqfMvLyltToxR/7uwEBvEMwAbz1/ZHeDweVVVV6b//+7/V09NDQD9psVhMt27dktPp1N69e+VyuWSaprq7u/UP//AP6uzs1J/+6Z/OyW5zAFgszFhU45031X78TQ3faFE0NCVXSqryVm9WWf0+pRWUyeF0slwDgG2GYTzwN2N9fX3Ky8tTbm5uoof4qZImoC3Lktfr1datW/Unf/In99fMxGIx/eQnP9HPfvYzffWrX9XKlSsTPVQAWBBCQ73qazmproZDmh4dkCxLmeXLVVK7W7mrquVK9XGmM4BHFolEdOvWrftfQ2KxmFpbW/Xzn/9c1dXV99dGz0dJE9AfMQzj/j/S7Aaa4uJiRaNRxWKxRA8PAOa9WHhaw9fOq6vhoEbvXJEZCcud5lfRxh0qWrdVaYVls8fSEc4AHpHD4dDIyIi+//3vKzU1VdJsw/l8PtXV1em1116T3+9P9DA/VVIFtGVZCgaDGhwcvD8DPTQ0pPfff1/bt29XaWlpoocIAPOWZZoKDvao89Qv1X/ptGbGR+RwupRdWaXyrS8rc8lKOT1eznQG8Ni2bNmiX/ziF4pEIvdnoB0Oh/Ly8lReXq60tLRED/EzJU1AG4ahcDisN998U4cOHbo/Az05OamlS5fqr//6r+fsqloASDaRqYAGrzSp7fgbCg31yYxF5cstUmndCypYu0WetHszQZbF6UZA0jBkGA5Jhqx7f60djtmbAR/nF0yGw3H/fT9Ndna2Nm/enOj/AI8saQJaml2u8eKLL+prX/ua3G63JGlwcFBvv/22fvSjH+kHP/jB/fvWAQCSGQ1r8Np59TYd1dC1c4qFp+X0pChn+VoVb9ypjJIKmbGYZsZHEj1UAHPMkKFwdEZGKChvOCqXGdb4aJ+sUFB6nBVahhQOBuQwTRmWpc8K6YVq3gW09YizG5Zlyel0asWKFXr55ZfvB7Qk1dfX67vf/a4OHjyo1atXz+urIQHgaTFjEV3573/W3ff+r8LjI7JkyeVNVVpBmaKhKfU2vy/r3DE93ndSAPOVYRiKxmNyD1zXyqEeSVJL9z/L7Xy8TrIkRQZ6lDYRlNc9IWsmlOiPOufmVUlaliWXy/XIEf3Re/z6mYLFxcWqqKhQR0eHpqenWcoBAJLMWExdH7yrie7bcri9SsnKV2pWriRDk71ts1+LEz1IAE+UJUupU6PKDYQUM2OaGAnMyfumhKNKDUfkmonIGY8n+mPOuXkV0MXFxXr11VcVjUZVUVHxSO/x0RW1v2p8fFx9fX2qq6u7f986ACx2DpdblS/+P8ooqVBqTqG8/iwZhoP5ZmARMSTlRqaVHujRdDSk2YUdj88Rico5Pq7cJStVunpToj/mnJtXAZ2VlaWvf/3rj/T/NQxDpmmqt7dXFy5ckMfjkSQFAgHt379fo6Oj2r59+8eWdgDAYuZwubX61T/U6ldfUzKuUQRgh3Vv4+Dc/gg9u6Ig+b6+zKuAflzxeFwHDx5UU1PT/SUgXq9XZWVl+rM/+7MFvdsTAJ6c5PvmBsAuQ7PpxNeDh2FYSXKFVDweV09Pj4aHhz+2BjolJUWFhYXKy8vj6CUAAAA8tqQJaAAAAOBpcCR6AAAAAMBCQkADAAAANhDQAAAAgA0ENAAAAGADAQ0AAADYQEADAAAANhDQAAAAgA0ENAAAAGADAQ0AAADYQEADAAAANhDQAAAAgA0ENAAAAGADAQ0AAADYQEADAAAANhDQAAAAgA0ENAAAAGADAQ0AAADYQEADAAAANhDQAAAAgA0ENAAAAGADAQ0AAADYQEADAAAANhDQAAAAgA0ENAAAAGADAQ0AAADYQEADAAAANhDQAAAAgA0ENAAAAGADAQ0AAADYQEADAAAANhDQAAAAgA0ENAAAAGADAQ0AAADYQEADAAAANhDQAAAAgA0ENAAAAGADAQ0AAADYQEADAAAANhDQAAAAgA0ENAAAAGADAQ0AAADYQEADAAAANhDQAAAAgA0ENAAAAGADAQ0AAADYQEADAAAANhDQAAAAgA0ENAAAAGADAQ0AAADYQEADAAAANhDQAAAAgA0ENAAAAGADAQ0AAADYQEADAAAANhDQAAAAgA0ENAAAAGADAQ0AAADY8P8B7JwsNj6ZNMwAAAAldEVYdGRhdGU6Y3JlYXRlADIwMTgtMDYtMTJUMTE6MDA6MzQrMDA6MDBkuYf/AAAAJXRFWHRkYXRlOm1vZGlmeQAyMDE4LTA2LTEyVDExOjAwOjM0KzAwOjAwFeQ/QwAAAABJRU5ErkJggg==)
Now, due to storm AC is broken and leans to make a shape as right-angled triangle shown in figure.
AC is the broken part of the tree and AB is the part which is still upright.
Hence,
Distance from tree foot to where top touches, BC = 8 m
And,
∠ BCA = 30o
Clearly, Sum of AB and AC will give the height of the tree.
In Δ ABC:
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
AC = ![](data:image/png;base64,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)
Hence,
![](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 = ![](data:image/png;base64,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)
Now,
Height of tree= AB + AC
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
rationalizing, we get
= 8√3 m
Hence, height of the tree is 8√3 m
Question 3.A contractor plans to install two slides for the children to play in a park. For the children below the age of 5 years, she prefers to have a slide whose top is at a height of 1.5 m, and is inclined at an angle of 30° to the ground, whereas for elder children, she wants to have a steep slide at a height of 3m, and inclined at an angle of 60° to the ground. What should be the length of the slide in each case?
Answer:![](data:image/png;base64,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)
In the first case:
Height of slide= 1.5 m and angle of elevation = 30°
Now,
![](data:image/png;base64,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)
where p = perpendicular, i.e. height of the slide and h = hypotenuse, i.e. length of the slide and θ is the angle of elevation
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Hence, h = 3 m
In the second case:
Height of slide, = 3 m, angle of elevation = 60°
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Hence, h = 2
m
Therefore, the length of the slide in the first case and the second case are 3 m and 2
respectively.
Question 4.The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of the tower, is 30°. Find the height of the tower
Answer:![](data:image/jpeg;base64,/9j/4AAQSkZJRgABAQEAYABgAAD/4RDuRXhpZgAATU0AKgAAAAgABAE7AAIAAAAMAAAISodpAAQAAAABAAAIVpydAAEAAAAYAAAQzuocAAcAAAgMAAAAPgAAAAAc6gAAAAgAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAGFobWFkIGF2YWlzAAAFkAMAAgAAABQAABCkkAQAAgAAABQAABC4kpEAAgAAAAM2MQAAkpIAAgAAAAM2MQAA6hwABwAACAwAAAiYAAAAABzqAAAACAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA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In this question:
b = 30 m,
Angle of elevation = 30°
And
p = height of tower = ?
[ p = perpendicular, b = base]
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Rationalizing the value of p, we get
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANYAAAA9CAYAAADRYJdvAAAI/UlEQVR4Xu2dBch1xRaGn9/uwMZGsAP72mJ3YGE3ooLK9arYKNiiiGJhYICtGNjd3Yp5r81VkXvtDl5d+3d/5z/7O3vPju/M3mtA5P/OzJqZd+adWWvNmj3j8OQIOAKVIzCucoku0BFwBHBi+SSIDYH7gQ+A/1TQ8OMqkNFXhBOrLmRdbh0ILAw8DMwF/FRHBVXJdGJVhaTLaQKBs4AfgUObqKxMHU6sMuh52SYRmBL4GFgO+HeTFYfU5cQKQc3LjAUCewBbAxtlVD4RsB2wEDAJMB0wK3ARcG/TDXZiNY241xeKwHPA8cDNfQRoHh8EPAI8m/p9S+Ba4FjgxNCKQ8o5sUJQg5DVcQlgR+Arq3IGW03fCmtCp0otD9wAzAf81qfn2qVEqquBfwK/WJ4pABFyHkD4v9cUak6s4kiHrI6rAKcAWkE/typnB26yifBE8WZ0qsTFZledkNHrfwDC8ENgSeD/lk8qof4uu2xV4LGmUHNiFUe66Oo4NfAMcKQRKV2jbIKjAE2Mb4s3pRMltLO/DywIfJrRYxFoZ3Nu3J3KMw3wEjAzsKj93ghoTqziMBddHbVLXQ7oDEZerXSSavOGGeW3FW9KJ0rIdlrJHBNFO6xyjwNnmmZQtHxwfidWceiKro5XAiubivJNT3XTA68AdwF7F29KJ0q8CewDPFiwt9rpbgXeBvYHvi9YvlR2J1Yp+EYU7rc6Tgw8CkwLLGuHm+lCOpt52VSc1TMM8+paGJ+ktYBzbbfP03rhvZs5ObY1TUG2beLMyCOjkjxOrEpgJGt1TIgjY1rE6x3g5PffgaWaXlWr6XqtUq6zEKazA2qRfXWS4b6n2VoBYsKKOLHCcFOpPKujCCdV778ZxEq8Vsonb1aj6kp410uX1O6sI4vR1LvZAB1FzJvy8hWteCrgaWAWU8ffLSogNL8TKxS5keWyVseZgFeBj5xY4wFbE7gR+Nrc4MnxQ+9IyFsq585eJYdIjgs5QOSyLysrd1OcWLmhGpix3+qosBrtWJ8NUAUlvAs7lmwmRULI/pHNuTawISBVOJ20m8nFvhnwwkDkYTVgPeACW8TSRfY1O+1FYAXg5xzySmdxYpWGcISA3tVRJ//PW45lgB96qktsLP1dh5iK3G5rmt/CjUSq++DPu4B3AA+ZLZTu9xbAEUaEQXhMbnIXz3CryyN4jqmEOqhvxJHhxBo0bBP+XmR11CDqYt7ctiN91yNO3kLtaLIltOK2PS0ApO0cHdwq5GgnC0lK+n8ncA1waQ5AEs+riLWrqZnpYuebu/5U4LAc8irJ4sQqBmPI6niynVEtYiphukaFNemc5QwLFC3Wmnbk1kJ1hamGXwAinxwOusyY15mjXVARLr1EFHGlSmpBk8MkK3KjciSdWMUgDVkd5UZ/ymLV0pHXqlnxa/cAK9p5VrHWtCf34YbFJoB2FuGsYNq8SfN4d2Bp4BbTAkRMxRZOBujKSRVX+fO2x795kRupvzMWXR016JcAiro4IGWo6+8X2iTSOUuvAR/QtIFFRHJ54T4ZmPMvd/gado70a478ZbKoLkWfyN6SB0+RKiFR/9q11rdIduEteVI1m8B2RP99xyo+HUJWR3kHpetLLZEhLRkimQJD9zPSFW9J8RLaBWSHyBM3Grk00XWHaWMjVxMBwrqUKM/d68A6xbs2XCX6EUt/E6CK4paaopAbAb2pnSv8D7iqKbflcME1ojVFV0fhKs+gXM66U/RAymPYVDcTwsjrlkWuPHnqaq/OuHT2p7tXUad+xNLAy9cvnVSXxxSdLd1XZJJHR6qQQvS36eM+LgKGBlB6sP4fmjRBdfja7/JbqMy2lxuNOGNJqlbh3kss/ftAQF/DkUflNeBJYPvUfaHk0FOuS93YDE1yj2plkqEamkSorcxYDZXRxXL9COSkqnAm9BJrDmADc1vqOrTcnnKHKkI7Scmhpn7TVfPYk2yJ2FIVH5pMiKToBqn+upoxmooYglFXsZ3AKyi7YVILepR35mDzsCRXnQWugiN19iL7S7tF7Kmzg29quPovB4pUatldChiuKnUW29G8grrRKjVNYKeTzl5ke+lQU8TzFC8CGv+j7cxINnXVxIoXmZItzyKWbrYqKlu21uk9dUgNOcZcoor58hQnAgmp5ISSx1e71rpOrmoGM4tYyXcddDlPzosk6f6QdiudZiugsTeotEirFjPbTXeRQpM+JaZQFX0wxFN+BNKk0gcw9XUj2VwKv3Jy5ccxM2cWsaTiyeunyZ++LyM1UAGSMngVXFomaSDnLOkVVESAPtAybO52LUyKAKgiVeGoSLejH6mS32Mg1zBjOx7nLGIpnF8d2NxCWlRgRkCflrrMogeqmDRtlTGsT81ovPUZth2M+NqpepPIdZodZA+jzTWs2I7AsR+xkuvkujSmeCsdCiuqW7q4SHV7W9lQUb+G+akZ3U3SfyKMLhJmpYRcUvd1GbGJkKY88A8ztgOJlXxtKLGvdD1aNtU7Q6hy5RmMpvMM81MzCqmSOz1vEK7sLTmoGrkcmGOghhnbgcT6l0VfKDLiyxyd9Sx/IxDVUzORDVxU2PYLaZJzQs6A3vOryMZhTJob1VMzY4JQeKVRYZsmllzp+i6BwpeuBw4xd/qwedzCh6b+klE9NVM/HJXWEBW2aWLtYu71BA0ZsOfF8HpepcMXLiy6p2bCu9p4yeiw9YuO1c2R6J6aqa7rtUuKDlsnVjVzIsqnZqrpeu1SosTWiVXNvIjyqZlqul67lCixdWJVMy+ifGqmmq7XLiVKbJ1Y5edFtE/NlO967RKixdaJVX5uRPvUTPmu1y4hWmydWNlzo/VPzdROiw5j68TqP/ideGpmjIjVCWydWBPOrs48NTMGxOoMtk6skbOrU0/NNEysTmHrxJpwdnXmqZmGiaXqOoOtEyvf7GrlUzP5ul57rlZi68TKP29a99RM/q7XnrN12Dqx8s+Z1j01k7/rtedsHbZOrGJzplVPzRTreu25W4WtE6v2+eIVdBEBJ1YXR937XDsCTqzaIfYKuoiAE6uLo+59rh0BJ1btEHsFXUTAidXFUfc+147AH8e0blyXcpk+AAAAAElFTkSuQmCC)
![](data:image/png;base64,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)
Hence the height of the tower is 10√3 m
Question 5.A kite is flying at a height of 60 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 60°. Find the length of the string, assuming that there is no slack in the string
Answer:![](data:image/jpeg;base64,/9j/4AAQSkZJRgABAQEAYABgAAD/4RDuRXhpZgAATU0AKgAAAAgABAE7AAIAAAAMAAAISodpAAQAAAABAAAIVpydAAEAAAAYAAAQzuocAAcAAAgMAAAAPgAAAAAc6gAAAAgAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAGFobWFkIGF2YWlzAAAFkAMAAgAAABQAABCkkAQAAgAAABQAABC4kpEAAgAAAAM3MwAAkpIAAgAAAAM3MwAA6hwABwAACAwAAAiYAAAAABzqAAAACAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA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To find: Length of String, AC
Given:
Height of kite from the ground = BC = 60 m, angle of elevation = 60° and length of string = AC = ?
Let the length of the string be h
Now we know that,
![](data:image/png;base64,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)
So in the given triangle,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Cross multiplying we get,
![](data:image/png;base64,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)
Hence, length of the string is 40√3 m
Question 6.A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from 30° to 60° as he walks towards the building. Find the distance he walked towards the building
Answer:![](data:image/png;base64,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)
Let AB be the boy, and CD be the building and angles becomes 60°, as the boy reaches E.
The angle of elevation in first case = 30°
And
The angle of elevation, in the second case = 60°.
Difference between bases in the first case and second case will give the distance covered by the boy.
1st case:
here p = height of the building - the height of the boy
= 30 - 1.5
= 28.5 m
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFMAAAAwCAMAAABaDLbGAAAAAXNSR0IArs4c6QAAAKJQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGaQAGa2OgAAOgA6OjoAOjpmOjqQOmaQOma2OpC2OpDbZgAAZgA6ZgBmZjoAZjo6ZjqQZpDbZrbbZrb/kDoAkDo6kDpmkGY6kGZmkLbbkNv/tmYAtmY6tpA6trZmttv/tv/btv//25A625Bm27Zm27aQ29u229v/2////7Zm/9uQ/9u2/9vb//+2///br8PuRgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAACLklEQVRYR+1XYVuCMBBmmCVZlpSaYmazrKUpEPv/f627Y9BAwM2HLz2P+6C43b27e2/jXh3nH4yvVz3I7bjwszZ+uR0x1iXbTZ8x90lZRh6D4Wog8Yh1Po144GzqxD4aC3cKuGyYukXerOgfDdbCFLMHroLNHBngk8Mv99WYaGaISQChhknIFXHaYnIMIAQWnE3G4EHulpjKfwtlyYsSeTeeql3Oq0XuMqC6RB58IbM05BxqF+h1t+FTFUcGWJ30Mxu0zd8wj5P3CCXx07rrtVVzGaoxpsDAwmEWYXaWOEZYjrNIhZ5C4Tm6hqsiEUGw+z2deYqOg38caEHLBd6si+ye1QJirngFGd0evJvdpWIhHsPsYN3kel47M9AiA+okljrC8Q3SA1weDX7VDvrs8U1btjg195bDKMEJjZOWdpJzM8lQ3I43qoJkorUA8zi56sSVHmHTYu0eqtvVrHNof5JesjYcJA8N1vIZRAB3lwfttJmGsPOxYt0aoRXdAp1ETt6wTUgVVy/rUq/UOnHelwu99RguNrZihyePnx1+rhQv8cKmTSU+hHKAGS8YJpw8EieJD63P4kxRXz7I/XuXSrT8JG09C81IOgN1Y2mkSupvOsyE7zEuYZ00SCZENHsJ2kG/mCV50oQMrmv5VqVfIHY6SUA2Fr8ilTrcaPIOkrNKekDdNnSSJKrHuKD9DPKvNhGsn9IZo2q6s6h7/ZYJ/TNpeYiT3kktB3GGq2HgFzJtLto6TDTgAAAAAElFTkSuQmCC)
b = 28.5√3
2nd case:
![](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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)
Hence, the distance covered by the boy:
= 28.5![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
= 19√3 m
Question 7.From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a 20 m high building are 45° and 60° respectively. Find the height of the tower.
Answer:![](data:image/png;base64,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)
Since the building is vertical.
∠QPO = 90°
In a right-angled triangle, we know,
![](data:image/png;base64,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)
In ∆OPQ,
tan 45° = ![](data:image/png;base64,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)
1 = ![](data:image/png;base64,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)
OP = 20 -------(1)
Now in ∆OPR
tan 60° = ![](data:image/png;base64,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)
=![](data:image/png;base64,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)
=![](data:image/png;base64,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)
20√3 = h+20
h = 20√3-20
h = 20(√3-1) m.
Therefore the height of transmission tower is 20(√3-1) m.
Question 8.A statue, 1.6 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60° and from the same point the angle of elevation of the top of the pedestal is 45°. Find the height of the pedestal.
Answer:Let AD be the height of the statue which is 1.6 m,
And DB be the height of the pedestal.
And C be the point where the observer is present.
![](data:image/png;base64,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)
To find: height of pedestal, BD
Now,
In Δ ABC,
![](data:image/png;base64,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)
where p = perpendicular and b = base
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIQAAAAwCAMAAADnwSL2AAAAAXNSR0IArs4c6QAAAK5QTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGaQAGa2OgAAOgA6OjoAOjo6OjpmOjqQOmaQOma2OpC2OpDbZgAAZgA6ZgBmZjoAZjo6ZjqQZpC2ZpDbZrbbZrb/kDoAkDo6kDpmkGY6kGZmkGaQkLaQkLbbkNv/tmYAtmY6tpA6tpBmtrZmttv/tv/btv//25A627Zm27aQ29u229v/2////7Zm/9uQ/9u2/9vb//+2///b81IyRQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAC50lEQVRYR+1Y63bTMAyO2xUIg3VQKOMSKLCljEJa1jiL3//F0C2x05LgJmkK50w/dqbNlj/r8klOEPwvkiqU59eEl5XRdFuPfvPmxvmnWYaPGhZ7OyEZ3QRZpF7SBlSCTfik3G2iD66lbK7GP+0f0vDyzvugpoUJWjUR2xbF3q4KQk9XtEIkDd/3AiEIYjqRXAAK+iCf1XpCYPLR7rpuYPIZBSJR6HZSsrkT5p1wVECktKcP0SFZYk/oEPPS9XETiHj8da7UZQ+JKTGOKdSomG8cGYgN1QrVi60ImxMmUi+2kMWc0p2EU0LCS0ol1A2eMBFtZQOdxESUhJwSrBwIwi2XllA4JTQzAyupcAZZbM4JDGEPnkgh3Pe3IWcXKsG6woH7ICg/yFsAfRusu5eInjmkzcrZWzfGVRBmgeVz9k5CpqE4Jkz4/7zEFao/PlxzeyF5kkxX5XHEw4OJiYA5pMr0s4JPTdQDlXjfoXqafioUl79yu7+3tZYLU7fNA/kIjaXjH0s1cSaAlua9tgnxAfMxmMIVyePPq/467l+gSC8s+auITgzUIhyP5PanjuR1Sa9FxHVFXuIvXBU0H1gQ+6ZKVJ1+EbsFCBlRCo9QVAYLR9HKyrKQoQ0zxA5AA4Wj7KsMgn720Oa8UoL7X3FqmRMwQ6/soORnaXdV4mSLX3VApWZfeFJCptRX30M1sRzeAob56M92lif4zDI3Wpxb2ZJfHTC81TBmVwxBekgDrOkdnUHE0ArN+hyGF5+wSBelU20X7QrCfIIaj0fX8Fp1xv56qzJPwAJ3nuiIQl9gjWNIeB4/iSTlOMKvo4Hlnt78S8mEbOFMa0MhyRaK3kGv6fo5jOFNH06OhOrXHbnfFugmPEU4ND50E5uMlXfZka6+Zxa/3bicTaAGF5gAqEBhKMLj+/sicshNYCBb0+UN8lTG3wEGl0Sdc0pk+ALt44NMiyvks1MUxC7Q5JAO2uKWD1sePHA6D/wGnBlOIxlkJQAAAAAASUVORK5CYII=)
In Δ DBC,
![](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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)
On comparing (i) and (ii),
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHYAAAAwCAMAAADzeH5SAAAAAXNSR0IArs4c6QAAAJZQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOjoAOjpmOjqQOmaQOma2OpC2OpDbZgAAZgBmZjoAZjo6ZjqQZpC2ZpDbZrbbZrb/kDoAkDo6kDpmkGY6kLaQkLbbkNv/tmYAtmY6tpA6tpBmttv/tv//25A627Zm27aQ29u229v/2////7Zm/9uQ/9u2/9vb//+2///bhyqeHgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAACQklEQVRYR+1X61rCMAxtAXUo6MTrFGEobAjrWN//5WyTyVpwHS3b/LzkF/loepKcrEkI+SmSUCnnE/AXlc5gXe798maq/Mln3qnhsCEJUWdK0oBewRGpkKV3VpznwaNinI5od1HoiTdcOeY3kvfwAG/LFSUCDZYN5nAil8R7cAQlJAQMCFMoMs7ML402dwzBtHOW+JkP6Y2ozCUo6UilS0+yBpuAjZswD2wxWubJitIyZ4ANuy8jSodOJZVzFQJlUuGvmG+ZcihsKO5t+Rbc8oBerkX9YTFaClKb0wSKTll5tDwAU7zAUngA5YPUomIJq5b2weBILcMvFZUk/4bxDiO3khinaBPB2ubNw7qQCon1d2cPFmiGjAhn1yR2KWfmK08jKr07jSsNlo9lqffucyKYKOQTfFb/lth2lLqyU9FR6oLZvaeiozQFW9FRGoKt6igNwRo7yldvez1+mDrKPsK2xRz1Y/tElneUeoLbvcXcURpLcmVHaSbayo5iCxsprJfaVncUS1j+pE7jlsbux7Nbh5HFHe7TMlFG5uNvO/iGUIw5PO6Ldt5msvmzGJfCzkRsScXMerDPzgfZhaAWNhScLVuSaDt74/zeuGxgg5zljKbjwbxxSLF+jSlM6tcQYiZGStOqXZtD7ytIavH5LL12kszkShUVZaTvCrXFt9/Kugv1ZQQ3WhCxNMPnI7YgCXjMDm3jrdgjYwiQy5cixa2yBYloH6lN5ebjtrQ7uJn57RTvrmvR93Qfhwz9m/y2DHwAvj05mv4ky+QAAAAASUVORK5CYII=)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
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)
Hence, height of pedestal is 0.8(√3 + 1)m
Question 9.The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 50 m high, find the height of the building
Answer:![](data:image/png;base64,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)
Let us take AB as building and
Let us take DC as tower = 50 m,
∠ACB = 30°
And,
∠ DBC = 60°;
AB= ?
In Δ DCB;
![](data:image/png;base64,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)
where, p = perpendicular and b = base
![](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 Δ ACB
![](data:image/png;base64,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)
where p = perpendicular and b = base
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHAAAAAwCAMAAAD+Zg4VAAAAAXNSR0IArs4c6QAAAJlQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOgBmOjoAOjpmOjqQOmaQOma2OpDbZgAAZgBmZjoAZjo6ZjpmZjqQZmaQZpC2ZrbbZrb/kDoAkDo6kDpmkGY6kJA6kLbbkNv/tmYAtmY6tpA6ttv/tv//25A625Bm27Zm27aQ29u229v/2////7Zm/9uQ/9u2/9vb//+2///b8/053AAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAACWklEQVRYR+1Y2VLDMAy0yxXuUsoVCBCO0BYSE///x6HDOWCaVGFQB2bwQ+uHrdey1iu5xvzt8XK/tv0XkYUxQkKfWHvwpM1cRFeBwsfbby7eeFZmbAhzDDO3Fb8Wb0OYYnDleEeLKaxbE+KJIiF+ao4i2o/sFhwmE/Kn5vDXl8bFkL51EVIwRXQcCPVzSIREE0RzrHmesHaKBBihyfBG6F+LFNLH1x0Fqq8Z407B2Q7J0NwEZsoaVc7XDywfzjxHx7ejNZxHZtkYMjTeeaTtg6ac3gZClNkaJPZwlXH9SjE2fZcoDt6YsBzDxXUTfd+95+SBU6BmLhsVpqSiunn4AXniEjmERWXaYJz+kaY9o97ENybsuHUEKddOZZFmaLtktj7+qhmNIy12US7UIXCbkFvVysJRmRdkoUTOIrlIs1YWe5L+CZbYEZUv6GELSubmhdjo/fUKefEmhDDBFSjPRHsTwgSEuUzOQpiAMEVlz/YstYfdQwhbTehvQN/p6I7bw84hhK3mM2DBwe6pbyITmfIbxoVvnC+BCRZfBiHHoEGdIQ4fb3EROGp+sAQ2mPD9FX/yEM7RJdw8MSPc4socu2HDGF1iyQJPKCy04lZPAoyLyQ5el17YIMbFKx1ho/Z51Hp++ji0K/2wQYyhw26enG37rQmrRnw5bBihhxa7bVjU4tdJXFQtQw9sGB9VM1I7iKQubp9Ew57XCRvKh2KcUVAe77yrX5+h4atk2gUbzIdPpD3OjUugDzqqTNyd86wI3x2wbxCWY9H/IkKYZAOZrFIIYRLGf8xvOYEPGMJABCEjtPYAAAAASUVORK5CYII=)
AB= 16.67 m
Question 10.Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60° and 30°, respectively. Find the height of the poles and the distances of the point from the poles
Answer:![](data:image/png;base64,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)
Let AB and DE be the two poles, and C be the point of observation.
Given,
width of road, BD = 80 m
Angle of elevation to AB, ∠ACB = 30°
Angle of elevation to DE, ∠ ECD = 60°
To find: Height of buildings AB and DE.
In Δ 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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)
![](data:image/png;base64,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)
In Δ EDC:
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHIAAAAsCAMAAACOhxzIAAAAAXNSR0IArs4c6QAAAJZQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOjoAOjpmOjqQOmaQOma2OpC2OpDbZgAAZgBmZjoAZjqQZpC2ZpDbZrbbZrb/kDoAkDo6kDpmkGYAkGY6kLbbkNv/tmYAtmY6tpA6tpBmttv/tv//25A625Bm27Zm27aQ29u229v/2////7Zm/9uQ/9u2/9vb//+2///bz6f99QAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAACaklEQVRYR+1Yf1PbMAy1A5QwfmUwRgaFbIDXjiYm/v5fbnqS0/RKa+IUc8cd/qO4nGNJT9LTS5X6tKvWsiYLJdtvd8ljMdm9Uq48JEPY2lKfp7Zp9p7IRHUNk9i6kv+RclWIT1ZF6EqsSVdbnCt3ixgVtjCp+Vu61eRUMgJlk7Ot5FEif80xAJVUErypcyn5W0llW/TJTQKudAcvv/2AVCJ/7XeCVFLZ5EOCNJ5A8CcWihodYTlUbF8e8tMl0Nvvcr/G91FTiLvUHbIdRnft5QC/YqMPn6+HgP++JkGPbnak9cF4gOM8cjdUbVV2R0WQmhw7x5g6mJuTd1Rn0izHW3KmUurlGWZ/+wza6cljXEqiT9upBppMHBg8Wp/0bLkkh3dN779nBrJvkXkeHgErHDVuy3RIaTT9PK3TqxaolFW2YxdkDKUBFkSsr2W6uhLG6Gt0RcQ+4MrJjANzYAFb9tM29qbh540+ksDslCTMkLEz/O4tJ9siSqeAiLMrhmWq9XGgjUW4Z77tOKD9n+KEiZkiJqOnZihrysjCBiUyy7y5KIQmnzzScyMKxWsb6CvWAsFq88Id1dEW/CmUE7c6k+Q5k0hQyvGckBPVDgxWawBLFwDXzvvNbrNwtxdyLCZ569fNqQrkPQt3yefmxRoeqd+x24UgqQzWTG7gKqTS/WFEdxmJvaEO2O2IsYZnSENYvFlLPinw2pfP1ndXqbTdTXp/EQBLlkCTiHCXySTAVuNerY0+WwgVoNVCiHHfznIur1pfdWl9E8jXB1h58q8P9mJVRKyfFOG+/0MK+i/YrlccI+x+PfKFgFL/AeUhNmRgnPpxAAAAAElFTkSuQmCC)
![](data:image/png;base64,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)
We know that AB = ED as the poles are of same height.
Hence, from (i) and (ii),
![](data:image/png;base64,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)
cross multiplying, we get
![](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,iVBORw0KGgoAAAANSUhEUgAAAFIAAAAYCAMAAABeMVqjAAAAAXNSR0IArs4c6QAAAIRQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOjqQOmaQOma2OpC2OpDbZgAAZgBmZjoAZpC2ZpDbZrbbZrb/kDoAkGY6kGZmkJBmkLaQkLbbkNv/tmYAtmY6tpA6ttv/tv//25A625Bm27Zm27aQ29v/2////7Zm/9uQ/9u2//+2///bgNKQ3QAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABXElEQVRIS+1Ty1aDMBBNoNIoFqst9UGwUpQA+f//c+5MwKMFXLhx0VlwCJm5uQ+i1KX+twNOo6Kbhml2B6P1ardE2ZcmQbM/aH19nOysokKpd7PGZmuSo6r1fgHSmfQD2z5Pmi6P36ZaK3xGg1J9xs+7yT6ZdSZIcGDipk+34NdneFq0LZb0oSyYYOlLnTS1ifb0IvN9tiELt0Jy6J+FHWl9yToVLn7a0fqxYCzYh3RYzU8ZlpPj9Ab2Nn7eap02wSkBrjQhWfIgQMJK/8ozrGWxfK5vG8py8w0Scz4nha3hYO0oWY78BZJbaGYQTkA+J5KM5pgTo4uLZ5DnwkMLlIV4RjToZHqBq4MbQbhli2dKvMFohf+H3effif1jerKu5T44/TDYOgfZmnUjdwH/cEgHx+AUSqdNVZsh0NW9mHjCbQxXcwa0pcCvXrDZ0Rt6mZtkXfKHS10c+KMDn/qoINHUAjA7AAAAAElFTkSuQmCC)
Now, using the value of BC in (i),
AB = 20√3 m
Now from triangle EDC,
![](data:image/png;base64,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)
Therefore,
Height of Pole = 20√3 m
Distances of poles from observing point = 60 m and 20 m
Question 11.A TV tower stands vertically on a bank of a canal. From a point on the other bank directly opposite the tower, the angle of elevation of the top of the tower is 60°. From another point 20 m away from this point on the line joining this point to the foot of the tower, the angle of elevation of the top of the tower is 30° (see Fig. 9.12). Find the height of the tower and the width of the canal
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)
Answer:
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)
According to this figure:
CD = 20 m,
∠ACB = 60°,
∠ ADB = 30°,
AB = ? and BD = ?
In Δ ABC,
![](data:image/png;base64,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)
where p = perpendicular and b = base of triangle
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGkAAAAsCAMAAABRyWbXAAAAAXNSR0IArs4c6QAAAJxQTFRFAAAA///b//+22///tv///9u229v//9uQttv/kNv//7Zm27aQ27ZmkLbbZrb/kLaQZrbb25Bm25A6tpA6ZpDbkJBmZpC2kJA6ZpCQOpDbOpC2tmY6kGaQtmYAZma2kGY6Oma2OmaQkDo6ZjqQAGa2kDoAZjpmOjqQZjoAADqQADpmZgBmADo6ZgAAOgBmOgA6OgAAAABmAAA6AAAAnqpenAAAAAF0Uk5TAEDm2GYAAAIgSURBVHja7Vdrb5tAEFw46JkLdWyaPqh7td3i+JHQHuz//2/V7h0FmjhKsVZqlewHCyPEam5mZweA/76i3VEBgEGqdqvkOhXInaBoM4ArV4k1im8/hk5N8hugSK3m3ALAEpq4FsOk98p3iusSID2IQYq+ZZ4g0I4EsRBjyZQAhjsRsugdX4rIoWZp0+stnZscTUXJkzQn0YkKQv9ImKF5+AGDpZA7MIIldmTlTkZ60RrbOdtQm2km7P6DgpdZ0cofcrRG3M+IXYen2WQGzyvDuM2bbgekuyaB+C6DfCrBOQn/XKPgI6whmhC9AYjvkmmISB6ky9zh6XqvohUeVe5IP/3EWbJL+suY9hMx2W5lLcBgBcvMNO8XvFFMh9bvl7ime9N5CoOmXdmNdEEzR3vFNtcHxI0KnR7sM4tdPctCeYOE89E/s3BJMol2+FnBlSvPdXq88PHq3N0jC6s4oAtvtkfVnd5lRjnYjb4dH6FhXNyJHgiK+GMc/vL0vCD4LUyQB8l3+f18WeAceoFMLNsk6fck2lUq/1SX+qsHaavoS6Jdpfy4kewuDjjay9a49gYsblRgjG/qA+LpLT2VHhC3/54lj4NrunaI90KhZRhctTvOnnI8uFzPA2OZapXPUFmfU6xYAoNxcBXMyTAOrkaKoJ6mEFz98ItVH1wlP2dgFFyFOw2Da7DOUsgiBsHV4I3ct8Y4uC7JirYvNcS+1hP1C+AOSnW4I0soAAAAAElFTkSuQmCC)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
In Δ ABD,
![](data:image/png;base64,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)
where p = perpendicular and b = base of triangle
![](data:image/png;base64,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)
![](data:image/png;base64,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)
𝐹rom (i) and (ii),
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Using the value of BC in (i) we get;
AB = 10√3 m which is the height of the tower
Width of canal = 10 m
Question 12.From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 45°. Determine the height of the tower.
Answer:![](data:image/png;base64,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)
Let us take AB as a building, with AB = 7 m
and CE as a cable tower
Angle of elevation from top of tree to top of cable tower∠EAD = 60°,
and angle of depression from the top of the building to the bottom of the tower is, ∠CAD = 45°
Also,
∠CAD = ∠ACB [Alternate angles]
Clearly,
AB = DC and EC = ED + DC ?
In Δ ABC:
![](data:image/png;base64,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)
where p = perpendicular and b = base, therefore
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGkAAAAsCAMAAABRyWbXAAAAAXNSR0IArs4c6QAAAJ9QTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOgA6OgBmOjpmOjqQOmaQOma2OpDbZgAAZgA6ZgBmZjoAZjo6ZjpmZjqQZmZmZma2ZpCQZpC2ZpDbZrbbZrb/kDoAkDo6kGY6kGaQkJA6kJBmkLaQkNv/tmYAtmY6tpA6ttv/tv//25A625Bm27Zm27aQ2////7Zm/9uQ/9u2//+2///bxWFS1AAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAACQklEQVRYR+1XaU/jQAx1wtEBCs0uN7Th2oSFNGQmmf//2/AxgWkloKQYCQl/iCIV5vnZb54dgB8fPt9ukIRNKNJ9eleKKmEkqNIC4MmMlGAAuuPbgLTxCBAIqqDdzyqCACiJTZepcXLjRpC6bALQHgo/hfBXhTQInCFBTBUw5EiLRCwjETP/n181ostY2nR8SXXTa1OFlPAmzUh0qoJwu6QFZxCJHwhK0F8fwgPmdDw3qzY60vPXSYpE0IbSwnHDNi+0NP4FZZpriZVziy4g69aaZOthYNY+f0cZzoSrThrC6P4WUA9tcE3CfyO67HQRyR0QGnvnZ8PnJA/SZY11+Tdu/D1OltqQfvCKT8RU5F70nMYDtcSGQQ2ZojRHMC/sxt1UJoodN0tI6/QpXDRnsFuSekV3juZK96cIRunMHjJell7Jo/vF4z4qJ08QPJnGidthVyT/RZmwVJBTNQN/NYU2X82SX+AXX3p3F2Y8vRiA2Mm2gRF6xLTXiGg2ChyX0Mps7hMRNSzP6E9WTwTBNeQGSWeCTHqkkn5YlxN2pT15RDpNfZ5N3JmUsBz5G2YlHlHis817ngMriJOe7MWa9BLK5KAJHQuew5aMO8cRtmt/qAsNzGyFf1tcXNtr3Fo2lZaWeHF1ZvsB3nO8FVJ/+0/CbZFthZ/DrPLjJKLFlbSkF9HiqreAcfrR4sq7mF5EiyvbqV68Lq6anzOYf7S4KiPFi6tUj21TIeLF1SaXet8ai4vrnKxI84NaoVS/R35LBZ4B+PA9zZVLbBQAAAAASUVORK5CYII=)
AB = BC = 7 m
In Δ EDA,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEkAAAAsCAMAAAAelGUHAAAAAXNSR0IArs4c6QAAAH5QTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOjoAOjpmOjqQOmaQOma2OpDbZgAAZgBmZjqQZrb/kDoAkDo6kDpmkGYAkGY6kLbbkNv/tmYAtmY6tpBmttv/tv//25A627Zm27aQ29u229v/2////7Zm/9uQ/9u2/9vb//+2///bcvKhpwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABmElEQVRIS+1W21LCMBBNUCyKVKlarJeg2Jbm/3/QvYSmF2SajTO8sC9smXJy9mT3LEqdM0rNMf9RnN5upHTM7FUpm93A7zGtM70SQpmrT/hlsUYkTG1GXwiiQDYcBZTIzCTRpCtlX5CRwhSRND0FR5WAylxPlRCElBNqU91hVSwT1CjUibXpyNSkXriQCvn6KVwqlwm1aR6gLpapSgaUjGtd/DjFscQrr4kYpvv35L6tlpk+TeuJKuUT4fo5Hc1K89hHDpGu/24p0//IgThGdrvQ+npalX9yts9wF8VsA1oKh+gATU1LoyntjgOSaS1G2vpK7XeI9ubUqfPlh+za6lxjSdSy6BJaL/1Utb06RbrvHVXje+ArOT3YnUnopTQ2IJHxVlWKXRlduDsqhMyeEVQdzqFes3HZDDHgUSY5Asy3RMNiU9aZN7JgRKMXTKPOwaIHHhGE1qQCH3Z2NijACHyAFqfbLUG8j7/sdks8kluc8UDijTk6urOvImlF9PDg5M4yjuPkBzQOR/6/YnTu/7UAbfVLnE+BX7R5GPd6C4TxAAAAAElFTkSuQmCC)
![](data:image/png;base64,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)
However,
The height of tower can be calculated as:
EC = ED + DC
= 7√3 + 7
= 7(√3 +1) m
Question 13.As observed from the top of a 75 m high lighthouse from the sea-level, the angles of depression of two ships are 30° and 45°. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships
Answer:
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)
A and D are the two ships and the distance between the ships is AD. BC is the lighthouse and is the height of the lighthouse. observer is at point C
Give: BC = height of lighthouse = 75m
∠CAB = 45°,
∠CDB = 30°
To Find: DA
In Δ ABC,
[ p = perpendicular and b = base of the right angled triangle]
![](data:image/png;base64,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)
AB=75 m [ tan 45º = 1]
In Δ CDB,
![](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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)
AD + AB= 75√3 m
![](data:image/png;base64,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)
DA = 75( √3 - 1) m
Hence the distance between the ships is 75( √3 - 1) m
Question 14.A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is 60°. After some time, the angle of elevation reduces to 30° (see Fig. 9.13).Find the distance traveled by the balloon during the interval.
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
From this figure:
BF = height of girl = 1.2 m,
AG = height of balloon from ground initially = 88.2 m,
AC = AG – GC
= 88.2 – 1.2
= 87 m
∠EBD = 30° and ∠ABC = 60°,
CD = ?
In Δ ABC;
![](data:image/png;base64,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)
where p = perpendicular and b is base
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEkAAAAsCAMAAAAelGUHAAAAAXNSR0IArs4c6QAAAI1QTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOjoAOjqQOmaQOma2OpC2OpDbZgAAZgBmZjoAZjqQZpC2ZpDbZrbbZrb/kDoAkDo6kDpmkGY6kLbbkNv/tmYAtmY6tpA6ttv/tv//25A625Bm27Zm27aQ29u229v/2////7Zm/9uQ/9u2/9vb//+2///b4y8nZQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAB30lEQVRIS+1Wa1eCQBDdxTLMih4mpVG6QQrE/v+f1zwWMUNhh87pS/MBOUf27szdO3dWqT+NdKJ1MIMUjKYYb4XpmOBRqVTfKJXMAaII8SkJG1/gsqTOxIzWEhhYUyMRnlJVBMkJI9dYXfDCy039IkHLQmDcAbkMJTBIMdRjNPOcu18JlI2Ra37uES+AqiI+Ozoyyk8aLhtWAeMdhBMsqfbkLkZfb1mZ7RKwT+40unPFbjlfEt9tEqjupd1zuHXuNNudUtcX2I2W8u5dZTukfYZDSIKlKuMh8kdhXAJNCVZYq7eriGP/m53CWiXSC/Zzg5+9OnbKxXTVa9mPj8qFxpKqW9JqFWk93akhYXOF6EPdx4aqaTSQhac9cIf+/QXzYJNovDinPpCEjUfr/VZp2tuvOmwePScNgOdgNgO8C2wipYIsirJ0FiYpD7Q4YZrKBTj01YBOriKvkZWzMJxaaPczmDYUxs8HaDBlIS0qwvEKbE84hmnqsglXET1Z1/5Bjc6DIemj/qM70Pwu7zglP14OMAugWON9ZZD26HyAJvtGZckdiLKjSUd11YPYn2pawXeK30DiOxw7BleXCM2DpmUa0jDP9aymzL/CAmwV2uOBu/MdW6VxWX+4/xViBr4AZrYiYTygTLgAAAAASUVORK5CYII=)
![](data:image/png;base64,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)
In Δ ABC,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEoAAAAwCAMAAACBtxzkAAAAAXNSR0IArs4c6QAAAJNQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOjoAOjpmOjqQOmaQOma2OpC2OpDbZgAAZgBmZjoAZjo6ZjqQZpC2ZpDbZrbbZrb/kDoAkDo6kDpmkGY6kLbbkNv/tmYAtmY6tpA6tpBmttv/tv//25A627Zm27aQ29u229v/2////7Zm/9uQ/9u2/9vb//+2///biZRmugAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAACC0lEQVRIS+1WW1vCMAxtwctQ1IlXFJwK3YRtrP//15lLN1o3aNEPXiQPUEZymp5mORFiH5bdvYXCpgMpe4/grSTZ2dKOLEeyPw+EUr0nIVJ5I0TyDCFFhJ+NFcOZCoXS43OMS+pc2oE7QxGgEFUM6bkWDCVyiQfsGWpVvVjDhUOJLALaDZI5rpNWOFQRwZGUZLJz821jBUPpMRLOnxb7FlYwVBXzDdKNU4a/pt3kw8XAgD9vsH0TbSd6ouT1kku0qxL0BC5FnuDLEGD44pxOifTg/QNgjy7/g4GE2y1YUPU03s5iC1XdAfD0UPTueMC9pGU0jbj42wb6JVhRfRtV947EbnHPuT6G6M/rC2o4jeVG1nxbYuvDMssiCsB1OaY22Bhqtqae5j0oqYBpy2Ztt2X9Cn8nvSls4S3tBPOpxYI6vCOrxSU8Ip9a4DaelJS9HBGGUXknRjWn7dQQG7dAGcBhBsxMMSar1QKfvRuGyslw5mEe6dEfTIMRT9q+nEg6+S3JWRVLSZe8zUgAHar4x9eCENelkEWeOYvnDY42s0dNFQ8T68Etd4uklR/Tw168LrjEELk/t9+azinAAiQVTSO6QFyvPqOrmhMYa6gUABR36ppyLKQC6AQdf8AAXluvDdRtSqWgsTpLM+x4uN/wt5IDpqrEyaHJ9jdgVRw6HPvRVXhX8IMdPQ7KwDc+oyodOa5logAAAABJRU5ErkJggg==)
![](data:image/png;base64,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)
Now, the distance covered by the balloon will be:
CD = BD – BC
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)
CD = 58√3 m
Question 15.A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30°, which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60°. Find the time taken by the car to reach the foot of the tower from this point.
Answer:The diagram is:
![](data:image/png;base64,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)
Let AB is the tower and AD is the highway.
Now from triangle ADB,
tan 30° = AB/AD
⇒ 1/√3 = AB/AD
⇒ AB = AD/√3 .............(1)
Again from triangle ACB
tan 60° = AB/AC
⇒ √3 = AB/AC
⇒ AB = AC√3 ........(2)
from equation 1 and 2
AD/√3 = AC√3
⇒ (DC + CA)/√3 = AC√3
⇒ DC + CA = AC√3×√3
⇒ DC + CA = 3AC
⇒ 3AC - Ac = CD
⇒ 2AC = CD
⇒ AC = CD/2
Since time taken by car to cover CD = 6 Second
So time taken by car to cover AC = 6/2 = 3 seconds.
Question 16.The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. Prove that the height of the tower is 6 m
Answer:In this figure
![](data:image/png;base64,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)
Let ∠ADB = θ and ∠ACB = 90°-θ [ As angles are complementary, their sum will be equal to 90°, and if one is θ other will be 90°-θ]
In Δ ABD;
![](data:image/png;base64,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)
![](data:image/png;base64,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)
In Δ ABC,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
But we know that,
And also by complementary angle formula that tan(90°-θ) = cot θ
tan(θ) tan(90°-θ) = 1
![](data:image/png;base64,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)
Therefore,
![](data:image/png;base64,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)
AB2 = 36
AB = 6 m
Hence proved.
A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is 30° (see Fig. 9.11)
Answer:
In this figure; AC is the rope which is 20 m long and we have to find AB (height of the pole).
In Δ ABC;
We know,
where p = perpendicular and h = hypotenuse
Hence, Height of the pole, AB = 10 m
Question 2.
A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30° with it. The distance between the foot of the tree to the point where the top touches the ground is 8 m. Find the height of the tree
Answer:
Let BAC be the tree.
Now, due to storm AC is broken and leans to make a shape as right-angled triangle shown in figure.
AC is the broken part of the tree and AB is the part which is still upright.
Hence,
Distance from tree foot to where top touches, BC = 8 m
And,
∠ BCA = 30o
Clearly, Sum of AB and AC will give the height of the tree.
In Δ ABC:
AC =
Hence,
AB =
Now,
Height of tree= AB + AC
=
=
= 8√3 m
Hence, height of the tree is 8√3 m
Question 3.
A contractor plans to install two slides for the children to play in a park. For the children below the age of 5 years, she prefers to have a slide whose top is at a height of 1.5 m, and is inclined at an angle of 30° to the ground, whereas for elder children, she wants to have a steep slide at a height of 3m, and inclined at an angle of 60° to the ground. What should be the length of the slide in each case?
Answer:
In the first case:
Height of slide= 1.5 m and angle of elevation = 30°
Now,
Hence, h = 3 m
In the second case:
Height of slide, = 3 m, angle of elevation = 60°
Hence, h = 2 m
Therefore, the length of the slide in the first case and the second case are 3 m and 2respectively.
Question 4.
The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of the tower, is 30°. Find the height of the tower
Answer:
In this question:
b = 30 m,
Angle of elevation = 30°
And
p = height of tower = ?
[ p = perpendicular, b = base]
Rationalizing the value of p, we get
Hence the height of the tower is 10√3 m
Question 5.
A kite is flying at a height of 60 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 60°. Find the length of the string, assuming that there is no slack in the string
Answer:
To find: Length of String, AC
Given:
Height of kite from the ground = BC = 60 m, angle of elevation = 60° and length of string = AC = ?
Let the length of the string be hNow we know that,
So in the given triangle,
Hence, length of the string is 40√3 m
Question 6.
A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from 30° to 60° as he walks towards the building. Find the distance he walked towards the building
Answer:
Let AB be the boy, and CD be the building and angles becomes 60°, as the boy reaches E.
The angle of elevation in first case = 30°
And
The angle of elevation, in the second case = 60°.
Difference between bases in the first case and second case will give the distance covered by the boy.
1st case:
here p = height of the building - the height of the boy
= 30 - 1.5
= 28.5 m
b = 28.5√3
2nd case:
Hence, the distance covered by the boy:
= 28.5
= 19√3 m
Question 7.
From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a 20 m high building are 45° and 60° respectively. Find the height of the tower.
Answer:
Since the building is vertical.
∠QPO = 90°
In ∆OPQ,
tan 45° =
1 =
OP = 20 -------(1)
Now in ∆OPR
tan 60° =
=
=
20√3 = h+20
h = 20√3-20
h = 20(√3-1) m.
Therefore the height of transmission tower is 20(√3-1) m.
Question 8.
A statue, 1.6 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60° and from the same point the angle of elevation of the top of the pedestal is 45°. Find the height of the pedestal.
Answer:
Let AD be the height of the statue which is 1.6 m,
And DB be the height of the pedestal.
And C be the point where the observer is present.
To find: height of pedestal, BD
Now,
In Δ ABC,
where p = perpendicular and b = base
In Δ DBC,
On comparing (i) and (ii),
Hence, height of pedestal is 0.8(√3 + 1)m
Question 9.
The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 50 m high, find the height of the building
Answer:
Let us take AB as building and
Let us take DC as tower = 50 m,
∠ACB = 30°
And,
∠ DBC = 60°;
AB= ?
In Δ DCB;
In Δ ACB
AB= 16.67 m
Question 10.
Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60° and 30°, respectively. Find the height of the poles and the distances of the point from the poles
Answer:
Let AB and DE be the two poles, and C be the point of observation.
Given,
width of road, BD = 80 m
Angle of elevation to AB, ∠ACB = 30°
Angle of elevation to DE, ∠ ECD = 60°
To find: Height of buildings AB and DE.
In Δ ACB
In Δ EDC:
We know that AB = ED as the poles are of same height.
Hence, from (i) and (ii),
cross multiplying, we get
Now, using the value of BC in (i),
AB = 20√3 m
Now from triangle EDC,
Therefore,
Height of Pole = 20√3 m
Distances of poles from observing point = 60 m and 20 m
Question 11.
A TV tower stands vertically on a bank of a canal. From a point on the other bank directly opposite the tower, the angle of elevation of the top of the tower is 60°. From another point 20 m away from this point on the line joining this point to the foot of the tower, the angle of elevation of the top of the tower is 30° (see Fig. 9.12). Find the height of the tower and the width of the canal
Answer:
According to this figure:
CD = 20 m,
∠ACB = 60°,
∠ ADB = 30°,
AB = ? and BD = ?
In Δ ABC,
In Δ ABD,
𝐹rom (i) and (ii),
Using the value of BC in (i) we get;
AB = 10√3 m which is the height of the tower
Width of canal = 10 m
Question 12.
From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 45°. Determine the height of the tower.
Answer:
Let us take AB as a building, with AB = 7 m
and CE as a cable tower
Angle of elevation from top of tree to top of cable tower∠EAD = 60°,
and angle of depression from the top of the building to the bottom of the tower is, ∠CAD = 45°
Also,
∠CAD = ∠ACB [Alternate angles]
Clearly,
AB = DC and EC = ED + DC ?
In Δ ABC:
where p = perpendicular and b = base, therefore
AB = BC = 7 m
In Δ EDA,
However,
The height of tower can be calculated as:
EC = ED + DC
= 7√3 + 7
= 7(√3 +1) m
Question 13.
As observed from the top of a 75 m high lighthouse from the sea-level, the angles of depression of two ships are 30° and 45°. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships
Answer:
A and D are the two ships and the distance between the ships is AD. BC is the lighthouse and is the height of the lighthouse. observer is at point C
Give: BC = height of lighthouse = 75m
∠CAB = 45°,
∠CDB = 30°
To Find: DA
In Δ ABC,
[ p = perpendicular and b = base of the right angled triangle]
AB=75 m [ tan 45º = 1]
In Δ CDB,
AD + AB= 75√3 m
DA = 75( √3 - 1) m
Hence the distance between the ships is 75( √3 - 1) m
Question 14.
A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is 60°. After some time, the angle of elevation reduces to 30° (see Fig. 9.13).Find the distance traveled by the balloon during the interval.
Answer:
From this figure:
BF = height of girl = 1.2 m,
AG = height of balloon from ground initially = 88.2 m,
AC = AG – GC
= 88.2 – 1.2
= 87 m
∠EBD = 30° and ∠ABC = 60°,
CD = ?
In Δ ABC;
In Δ ABC,
Now, the distance covered by the balloon will be:
CD = BD – BC
CD = 58√3 m
Question 15.
A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30°, which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60°. Find the time taken by the car to reach the foot of the tower from this point.
Answer:
The diagram is:
Let AB is the tower and AD is the highway.
Now from triangle ADB,
tan 30° = AB/AD
⇒ 1/√3 = AB/AD
⇒ AB = AD/√3 .............(1)
Again from triangle ACB
tan 60° = AB/AC
⇒ √3 = AB/AC
⇒ AB = AC√3 ........(2)
from equation 1 and 2
AD/√3 = AC√3
⇒ (DC + CA)/√3 = AC√3
⇒ DC + CA = AC√3×√3
⇒ DC + CA = 3AC
⇒ 3AC - Ac = CD
⇒ 2AC = CD
⇒ AC = CD/2
Since time taken by car to cover CD = 6 Second
So time taken by car to cover AC = 6/2 = 3 seconds.
Question 16.
The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. Prove that the height of the tower is 6 m
Answer:
In this figure
Let ∠ADB = θ and ∠ACB = 90°-θ [ As angles are complementary, their sum will be equal to 90°, and if one is θ other will be 90°-θ]
In Δ ABD;
In Δ ABC,
But we know that,
And also by complementary angle formula that tan(90°-θ) = cot θ
tan(θ) tan(90°-θ) = 1
Therefore,
AB2 = 36
AB = 6 m
Hence proved.