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As observed from the top of a 75 m 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.
Let CD be the lighthouse whose height is 75 m. Let the two ships be at A and B such that their angles of depression from D are 30° and 45° respectively.
Let AB = x m and BC = y m
In right triangle BCD, we have
In right triangle ACD, we have
Comparing (i) and (ii) we get
Hence, the distane between two ships be
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