A guard stands on the edge of a vertical cliff 40 m above the sea. Ignoring his own height, he sees a boat on the water at an angle of depression of \(30^\circ\). How far is the boat from the foot of the cliff?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(40\sqrt{3}\) m
The angle of depression is measured down from the horizontal at the guard's eye. The horizontal is parallel to the sea, so the line of sight meets the sea at the same \(30^\circ\) (alternate angles). In the right-angled triangle, the cliff is opposite this angle and the distance is next to it.
\(\tan 30^\circ=\displaystyle\frac{40}{d}\)
\(d=\displaystyle\frac{40}{\tan 30^\circ}=40\sqrt{3}\) m
