From the top of a lighthouse 50 m high, the angle of depression of a boat in the sea is 30°. Find the distance of the boat from the foot of the lighthouse. \((\sqrt{3} = 1.73)\)

Q.3 (B)(4) From the top of a lighthouse 50 m high, the angle of depression of a boat in the sea is 30°. Find the distance of the boat from the foot of the lighthouse. \((\sqrt{3} = 1.73)\)

Doubtly AI Asked 27 Oct 2026 AI-generated · not yet verified ssc 10th Save WhatsApp Report

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Answer: \(50\sqrt{3}\) m \(\approx\) 86.5 m

Let AB be the lighthouse with top A and foot B, and let C be the boat. AB = 50 m, ∠ABC = 90°.

The angle of depression from A equals the angle of elevation from C (alternate angles), so ∠ACB = 30°.

In right Δ ABC, \(\tan 30^\circ = \dfrac{AB}{BC} \Rightarrow \dfrac{1}{\sqrt{3}} = \dfrac{50}{BC} \Rightarrow BC = 50\sqrt{3}\).

\(BC = 50 \times 1.73 = 86.5\) m.

Doubtly AI · 27 Oct 2026 AI-generated · not yet verified Report

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From the top of a lighthouse 50 m high, the angle of depression of a boat in the sea is 30°. Find the distance of the boat from the foot of the lighthouse. \((\sqrt{3} = 1.73)\)

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