A house subtends a right angle at the window of an opposite house and the angle of elevation of the window for the bottom of the first house is `60^@` If the distance between the two houses be `6m` then the height of the first house is

Options

A. `8sqrt3`m
B. `6sqrt3`m
C. `4sqrt3`m
D. none of these

Answer

A

Explanation

Let PQ be the house subtending a right angle at the window B of opposite house AB.
In `trianglePAB`, we have
`tan 60^@=(AB)/6 rArr AB=6sqrt3`m
In `triangleCBQ`, we have
`tan 30^@=(h-CP)/(BC)`
`rArr 1/sqrt3=(h-6sqrt3)/6`
`rArr h=6(sqrt3+1/sqrt3)m`
`rArr h=8sqrt3`m