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Height and Distance
Height and Distance
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Question

Two poles standing on a horizontal ground are of heights 5m and 10 m respectively. The line joining their tops makes an angle of 15º with ground. Then the distance (in m) between the poles, is :-

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Solution

tan⁡15o=5d⇒d=5tan⁡15o\tan {15^o} = {5 \over d} \Rightarrow d = {5 \over {\tan {{15}^o}}} ⇒5(3+1)3−1⇒5(4+23)2 \Rightarrow {{5\left( {\sqrt 3 + 1} \right)} \over {\sqrt 3 - 1}} \Rightarrow {{5\left( {4 + 2\sqrt 3 } \right)} \over 2} =5(2+3) = 5\left( {2 + \sqrt 3 } \right)

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