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Height and Distance
Height and Distance
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Question

A vertical pole fixed to the horizontal ground is divided in the ratio 3 : 7 by a mark on it with lower part shorter than the upper part. If the two parts subtend equal angles at a point on the ground 18 m away from the base of the pole, then the height of the pole (in meters) is :

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Solution

Let height of pole = 10ll tan⁡α=3l18=l6\tan \alpha = {{3l} \over {18}} = {l \over 6} tan⁡2α=10l18\tan 2\alpha = {{10l} \over {18}} 2tan⁡α1−tan⁡2α=10l18{{2\tan \alpha } \over {1 - {{\tan }^2}\alpha }} = {{10l} \over {18}} use tan⁡α=l6⇒l=725\tan \alpha = {l \over 6} \Rightarrow l = \sqrt {{{72} \over 5}} height of pole = 10l=121010l = 12\sqrt {10}

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