A window in a building is at a height of 10 meters from the ground. The angle of depression of a point P on the ground from the window is 30°. The angle of elevation of the top of the building from the point P is 60°. What is the height of the building? ​​

Correct option is A

Given:
Height of the window from the ground = 10 m
Angle of depression of point P from the window = 30°
Angle of elevation of the top of the building from point P = 60°

Formula used:

$$\tan\theta = \frac{\text{P}}{\text{B}}$$​

Where,

P = Perpendicular or height

B = Base
Solution:

In Triangle QPB,

​$$\tan 30^\circ = \frac{\text{height of the window}}{\text{horizontal distance} (x)}$$

$$\frac{1}{\sqrt{3}} = \frac{10}{x}$$

$$x = 10\sqrt{3}$$

In Triangle APB,

​$$\tan 60^\circ = \frac{\text{additional height} (h)}{\text{horizontal distance} (x)}$$

$$\sqrt{3} = \frac{h}{10\sqrt{3}}$$​​​

​​​​h = 30

So, the height of the building is 30m.

Thus, the correct answer is (a).