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 beta)/(cot beta - cot alpha)`
B. `(h cot alpha)/(cot alpha-cot beta)`
C. `(h tan alpha)/(tan alpha - tan beta)`
D. None of the above

Answer

B

Explanation

In `DeltaBDC`,
`tan beta = (CD)/(BD)=(H)/(BD)`
`BD=(H)/(tan beta)=H cot beta`
In `DeltaALC`,
`tan alpha = (CL)/(AL)=(H-h)/(BD)`
`BD= (H-h)cot alpha`
from (i) & (ii),
`(H-h) cot alpha =H cot beta`.
`H cot alpha - h cot alpha = H cot beta`.
`H[ cot alpha - cot beta]=h cot alpha`.
`H=(h cot alpha)/(cot alpha-cot beta)`