A tower stands vertically on the ground. From a point on the ground which is 18 m away from the foot of the tower, the angle of elevation of the top of the tower is found to be 30°. Find the height of the tower.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(6\sqrt{3}\) m
The tower, the ground and the line of sight form a right triangle. The height is the side opposite the 30° angle and the 18 m is the side next to it, so the ratio that links them is the tangent: \(\tan30^\circ=\frac{\text{height}}{\text{distance}}\).
With \(h\) the height of the tower: \(\displaystyle \tan30^\circ=\frac{h}{18}\), and \(\tan30^\circ=\frac{1}{\sqrt{3}}\)
Height of the tower: \(\displaystyle h=\frac{18}{\sqrt{3}}=\frac{18\sqrt{3}}{3}=6\sqrt{3}\) m