The angle of elevation of the top of a building from a point P on the horizontal is 30°. If the point P is 48 m away from the foot of the building, then what is the height of the building?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(16\sqrt{3}\) m
The building, the ground and the line of sight from P form a right triangle. In it, the height is the side opposite the 30° angle and the 48 m is the side next to it, so \(\tan 30^\circ\) links them.
\(\displaystyle \tan30^\circ=\frac{h}{48}\), and \(\displaystyle \tan30^\circ=\frac{1}{\sqrt3}\)
\(\displaystyle h=\frac{48}{\sqrt3}=\frac{48\sqrt3}{3}=16\sqrt3\) m