question_answer

The top of a hill when observed form the top and bottom of a building of height h is at angles of elevation p and q respectively. What is the height of the hill?

A) \[\frac{h\cot q}{\cot q-\cot p}\]

B) \[\frac{h\cot p}{\cot p-\cot q}\]

C) \[\frac{2h\tan p}{\tan p-\tan q}\]

D) \[\frac{2h\tan q}{\tan q-\tan p}\]

Correct Answer: B

Solution :

[b]

Let height of hill = H

& horizontal distance between building & hill = d

\[\tan q=\frac{H}{d}\Rightarrow d=\frac{H}{\tan q}=H\cot q\]

\[\tan p=\frac{(H-h)}{d}\Rightarrow d=(H-h)cot\,\,p\]

\[\Rightarrow H\cot q=(H-h)cot\,\,p\]

\[H=\frac{h\,\,\cot p}{\cot \,\,p-cot\,\,q}\]