The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 50 m high, find the height of the building.

50/3 m

The correct answer is Option (3) → 50/3 m

Step 1: Let the height of the building = h m

Height of the tower = 50 m
Distance between the building and tower = x m

Step 2: Use tan of angles of elevation

1. From foot of tower to top of building: angle = 30°

$\tan 30^\circ = \frac{\text{height of building}}{\text{distance between them}} = \frac{h}{x}$

$\frac{1}{\sqrt{3}} = \frac{h}{x} \Rightarrow h = \frac{x}{\sqrt{3}} \quad …(1)$

1. From foot of building to top of tower: angle = 60°

$\tan 60^\circ = \frac{\text{height of tower}}{\text{distance between them}} = \frac{50}{x}$

$\sqrt{3} = \frac{50}{x} \Rightarrow x = \frac{50}{\sqrt{3}} \quad …(2)$

Step 3: Find height of building

Substitute $x = \frac{50}{\sqrt{3}}$​ into (1):

$h = \frac{x}{\sqrt{3}} = \frac{50/\sqrt{3}}{\sqrt{3}} = \frac{50}{3} \ \text{m}$