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 ${60}^{\circ }$ and from the same point the angle of elevation of the top of the pedestal is ${45}^{\circ }$. Find the height of the pedestal.

• A. 2 / (√3−1) m
• B. 2 / (√3 +1) m
• C. 4 / (√3−1) m
• D. 4 / (√3 + 1) m

Answer 1

The correct option is A

2 / (√3−1) m

CD = 2m

Let BC = x

AB = x (using tan ${45}^{\circ }$)

In $\Delta$ABD

BD = AB $\sqrt{3}$ = x$\sqrt{3}$

We know CD = BD - BC = 2m

$\Rightarrow$ x($\sqrt{3}$ - 1) = 2

$\Rightarrow$ x = $\frac{2}{(\sqrt{3}-1)}$m, which is the height.