Question

A tower subtends an angle of ${30}^{\circ }$ at a point on the same level as its foot. At a second point 'h' meters above the first point, the angle of depression of the foot of the tower is ${60}^{\circ }$. The height of the tower is:

• A. $\frac{h}{2}$ m
• B. $\frac{h}{3}$ m
• C. $\sqrt{3}h$ m
• D. $\frac{h}{\sqrt{3}}$ m

Answer 1

The correct option is B

$\frac{h}{3}$ m

Let the height of tower be H

In triangle ABC

$tan{30}^{\circ }=\frac{AB}{AC}=\frac{H}{AC}$......... 1

In triangle ADC

$tan{60}^{\circ }=\frac{CD}{AC}=\frac{h}{AC}$..........2

Divide 1 by 2

We get $\frac{tan{30}^{\circ }}{tan{60}^{\circ }}=\frac{H}{h}$

$H=\frac{h}{3}$