From the top of a 60 m high building, the angles of depression of the top and bottom of a lamp post are 30° and 60°, respectively. Find the height of the lamp post.​

Correct option is A

Given:

Height of building = 60 m;

Angle of depression to top of lamp post = 30°

Angle of depression to bottom of lamp post = 60°

Required: Height of the lamp post.

Formula Used:

​$$\tan(\theta) = \frac{\text{Perpendicular}}{\text{Base}}$$​​

Solution:

Let the horizontal distance between building and lamp post be x

From top of building to top of lamp post:

​$$\tan(30^\circ) = \frac{60 - h}{x}$$​​

​$$\frac{1}{\sqrt{3}} = \frac{60 - h}{x}$$​​

​$$60 - h = \frac{x}{\sqrt{3}} .......\tag{1}$$​​

From top of building to bottom of lamp post:

​$$\tan(60^\circ) = \frac{60}{x}$$​​

​$$\sqrt{3} = \frac{60}{x}$$​​

​$$x = \frac{60}{\sqrt{3}}...... \tag{2}$$​​

Substitute (2) into (1):

​$$60 - h = \frac{60/\sqrt{3}}{\sqrt{3}} = \frac{60}{3} = 20$$​​

h = 60 - 20 = 40 m

Thus, height of the lamp post is 40 m