The top of a hill when observed from 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 ?

Options

A. `(h cot q)/(cot q- cot p)`
B. `(h cot p)/(cot P - cot q)`
C. `(2h tan p)/(tan p - tan q)`
D. `(2h tan q)/(tan q-tan p)`

Answer

B

Explanation

Let height of hill = H
& horizontal distance between building & hill = d
`tan q = (H)/(d) rArr d = (H)/(tan q)=H cot q`
`tan p = ((H-h))/(d) rArr d = (H-h)cot p`
`rArr H cot q = (H-h) cot p`
`H=(h cot p)/(cot p - cot q)`