question_answer

The top of a hill observed from the top and bottom of a building of height h is at the angle of elevation p and q respectively. The height of the hills is [UPSEAT 2001; EAMCET 1989]

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

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

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

D) None of these

Correct Answer: B

Solution :

Let AD be the building of height h and BP be the hill then \[\tan q=\frac{h+x}{y}\] and \[\tan p=\frac{x}{y}\] Þ  \[\,\tan q=\frac{h+x}{x\cot p}\] \[\Rightarrow \,\,x\cot p=(h+x)\cot q\] Þ  \[x=\frac{h\cot q}{\cot p-\cot q}\] Þ  \[h+x=\frac{h\cot p}{\cot p-\cot q}\].