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.
Answer & explanation
Correct answer: option 3
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
- From foot of tower to top of building: angle = 30°
$\tan 30^\circ = \frac{\text{height of building}}{\text{distance between them}} = \frac{h}{x}$
$\frac{1}{\sqrt{3}} = \frac{h}{x} \Rightarrow h = \frac{x}{\sqrt{3}} \quad …(1)$
- 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):
$h = \frac{x}{\sqrt{3}} = \frac{50/\sqrt{3}}{\sqrt{3}} = \frac{50}{3} \ \text{m}$