A tower is 20 m high. The angle of elevation of the top of the tower from a point on the ground is 30°. Find the distance of the point from the base of the tower.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 20\(\sqrt{3}\) m
The tower, the ground and the line of sight form a right-angled triangle. With the angle of elevation at the point P, the tower TB is the side opposite the angle and the distance PB is the side adjacent to it, so the two are linked by the tangent of the angle.
Tangent of the angle at P: \(\tan 30^\circ=\displaystyle\frac{TB}{PB}=\frac{20}{PB}\)
Since \(\tan 30^\circ=\displaystyle\frac{1}{\sqrt{3}}\), the distance is \(PB=20\sqrt{3}\,\mathrm{m}\)