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Question:

As observed from the top of a 75m high lighthouse from the sea-level, the angles of depression of two ships are 30° and 45°. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships.

Solution:

In ΔABC, AB/BC = tan 45°, BC = 75m
In ΔABD, AB/BD = tan 30° ⇒ 75/(BC+CD) = 1/√3 ⇒ 75/(75+CD) = 1/√3
∴ CD = [75(√3 - 1)]m