From a point 60 m away from the foot of a building, the angle of elevation of the top of the building is 30°. What is the height of the building?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(20\sqrt{3}\) m
The building, the ground and the line of sight form a right triangle. The height is the side opposite the 30° angle and the 60 m distance is the side next to it, so \(\tan30^\circ=\frac{\text{height}}{\text{distance}}\).
From the triangle: \(\displaystyle\tan30^\circ=\frac{h}{60}\), where \(\displaystyle\tan30^\circ=\frac{1}{\sqrt{3}}\)
Height of the building: \(\displaystyle h=\frac{60}{\sqrt{3}}=\frac{60\sqrt{3}}{3}=20\sqrt{3}\) m