The angle of elevation of the top of a hill at the foot of a tower is 60° and the angle of elevation

Let  be the height of hill. And  be the tower of heightm. Angle of elevation of the top of hill from the foot of tower is 60° and angle of elevation of top of tower from foot of hill is 30°. Let  and,

Here we have to find height of hill.

The corresponding figure is as follows

So we use trigonometric ratios.

In,

$\Rightarrow \quad \tan 30^{\circ}=\frac{C D}{A C}$

$\Rightarrow \quad \frac{1}{\sqrt{3}}=\frac{50}{x}$

$\Rightarrow \quad x=50 \sqrt{3}$

Again in $\triangle A B C$

$\Rightarrow \quad \tan 60^{\circ}=\frac{A B}{A C}$

$\Rightarrow \quad \sqrt{3}=\frac{h}{x}$

$\Rightarrow \quad h=x \sqrt{3}$

$\Rightarrow \quad h=150$

Hence the height of hill is $150 \mathrm{~m}$.