Chapter: Trigonometry· Mathematics Part 2 (Geometry)
Answer: \(30\sqrt3 = 51.9\) m
[Figure: Lighthouse AB = 30 m with top A, foot B; boat at C on the water. The angle of depression at A equals \(\angle ACB = 30^\circ\) (alternate angles).]
In right-angled ΔABC: \(\tan 30^\circ = \dfrac{AB}{BC}\) \(\therefore \dfrac{1}{\sqrt3} = \dfrac{30}{BC}\) \(\therefore BC = 30\sqrt3 = 30 \times 1.73 = 51.9\) m.