Question

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

• 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 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

Divide 1 by 2

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

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