The angle of depression of a point situated at a distance 100 m from the base of a pole is 30°. Find the height of the pole.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\frac{100}{3}\sqrt{3}\) m
The angle of depression of the point C, seen from the top A of the pole, equals the angle of elevation of A seen from C, because the horizontal line at A is parallel to the ground. In the right triangle ABC, \(\tan30^\circ=\frac{\text{height}}{\text{distance}}\).
\(\displaystyle \tan30^\circ=\frac{h}{100}\), and \(\displaystyle \tan30^\circ=\frac{1}{\sqrt{3}}\)
\(\displaystyle h=\frac{100}{\sqrt{3}}=\frac{100\sqrt{3}}{3}\) m (about 57.7 m)