The angle of elevation of top of a tower from a point on the ground is `30^@` and it is `60^@` when it is viewed from a point located 40 m away from the initial point towards the tower the height of the tower is

Options

A. `20sqrt3` m
B. `sqrt3/20` m
C. `10sqrt3`m
D. `sqrt3/10` m

Answer

A

Explanation

Let AB be the tower of height h metre and C be a point on the ground such that the angle of elevation of B from C is `30^@`.

In `triangleDAB`, we have
`tan 60^@ =h/(AD) rArr AD=h/sqrt3` m
Now, `AC=hsqrt3`m
`rArr AD+DC = hsqrt3`
`rArr h/sqrt3+40=hsqrt3 rArr h(sqrt3-1/3)=40 rArr h=20sqrt3` m