A tower stands at the centre of a circular park . A and B are two points on the boundary of the park such that AB(=a) subtends an angle of `60^@` at the foot of the tower , and the angle of elevation of the top of the tower from A or B is `30^@`. The height of the tower is

Options

A. `a/sqrt3`
B. `sqrt3a`
C. `(2a)/sqrt3`
D. `2sqrt3a`

Answer

A

Explanation

Let OP be the tower of height h . In `triangleOAP` , we have
`tan 30^@=(OP)/(OA) rArr 1/sqrt3=h/a rArr h=a/sqrt3`