A tower stands vertically on the ground. From a point on the ground, which is 15 m away from the foot of the tower, the angle of elevation of the top of the tower is found to be 60°. Find the height of the tower in meter.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(15\sqrt{3}\)
The tower, the ground and the line of sight form a right-angled triangle. With the angle of elevation at the observer, the height is the side opposite the angle and the distance from the foot is the side next to it, so tan of the angle = height ÷ distance.
In triangle ABC, \(\displaystyle \tan60^{\circ}=\frac{h}{15}\)
Since \(\tan60^{\circ}=\sqrt{3}\), the height is \(h=15\sqrt{3}\) m