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 to the foot of the first tower is ${60}^{\circ }$. The height of the tower is:

• A. h/2 m
• B. h/3 m
• C. √3h
• D. h/√3

Answer 1

The correct option is B

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 = $\frac{h}{3}$