Question

Two towers A and B are standing at some distance apart. From the top of tower A, the angle of depression of the foot of tower B is found to be ${30}^{\circ }$. From the top of tower B, the angle of depression of the foot of tower A is found to be ${60}^{\circ }$. If the height of tower B is ‘h’ m then the height of tower A in terms of ‘h’ is _____ m

• 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 A be = AB = H.

And the height of tower B = CD = 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)

Dividing (1) by (2) we get, $\frac{tan{30}^{\circ }}{tan{60}^{\circ }}$ = $\frac{H}{h}$

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