Question

Two towers A and C are standing at some distance apart. From the top of tower A, the angle of depression of the foot of tower C is found to be 30°. From the top of tower C, the angle of depression of the foot of tower A is found to be 60°. If the height of tower C is ‘h’ m, then the height of tower A in terms of ‘h’ 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 A = AB = $\text{H}$.

And the height of tower B = CD = $h$

In triangle ABC,

$tan{30}^{\circ }$ = $\frac{AB}{AC}$ = $\frac{\text{H}}{AC}$$⟶\left(1\right)$

In triangle ADC,

$tan{60}^{\circ }$ = $\frac{CD}{AC}$ = $\frac{h}{AC}$$⟶\left(2\right)$

Dividing (1) by (2) we get,
$\frac{tan{30}^{\circ }}{tan{60}^{\circ }}=\frac{\text{H}}{h}\text{H}=\frac{h}{3}$