Question

A statue, 2 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60° and from the same point, the angle of elevation of the top of the pedestal is 45°. Find the height of the pedestal.

Options

• `2 (sqrt3 + 1)`

• `2 (sqrt3 - 1)`

• `1/(2 (sqrt3))`

• `(sqrt3 + 1)/2`

Answer 1

`2 (sqrt3 - 1)`

Explanation:

CD = 2 m

Let BC = x

AB = x (using tan 45°)

In `Delta "ABD"`

BD = AB `sqrt3 = "x" sqrt3`

We know CD = BD – BC = 2m

`"x" (sqrt3 - 1)`

`"x" = 2 (sqrt3 - 1),` which is height