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Previous Year Question (PYQs)

The top of a hill observed from the top and bottom of a building of height $h$ is at angles of elevation $p$ and $q$ respectively. The height of the hill is:




Solution

Let height of hill be $H$ and horizontal distance be $x$. From bottom of building: $\tan q = \dfrac{H}{x}$ From top of building: $\tan p = \dfrac{H-h}{x}$ Subtracting: $x(\tan q - \tan p)=h$ So, $H = \dfrac{h\tan q}{\tan q-\tan p} = \dfrac{h\cot p}{\cot p-\cot q}$

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