The angle of elevation of the top of a building from the foot of a tower is 30°. The angle of elevation of the top of the tower when seen from the foot of the building is 60°. If the tower is 60 m high, then the height of the building is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 20 m
Step 1: Draw the situation
- Let the height of the building be h m.
- Height of the tower = 60 m.
- Let the distance between the tower and the building = x m.
We have a right triangle situation:
From foot of tower: angle of elevation to building top = 30° →
$\tan 30° = \frac{h}{x} ⇒\frac{1}{\sqrt{3}} = \frac{h}{x} ⇒x = \sqrt{3} h$
From foot of building: angle of elevation to tower top = 60° →
$\tan 60° = \frac{60}{x} ⇒\sqrt{3} = \frac{60}{x} ⇒x = \frac{60}{\sqrt{3}} = 20 \sqrt{3} \, \text{m}$
Step 2: Equate the two expressions for x
$x = \sqrt{3} h = 20 \sqrt{3} ⇒h = 20 \, \text{m}$