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.

Answer 1

this is solution of this question

Answer 2

[75 ($\sqrt{3}- 1$)] m is the distance between two ships.

Explanation:

In the given ΔABC,

BC(height) = 75m

AB/BC = Tan 45° = 1

While in the given ΔABD,

AB/BD = Tan 30°

⇒ 75/(BC + CD) = 1/$\sqrt{3}$

⇒ 75/(75 + CD) = 1/$\sqrt{3}$

∴ CD = BD - BC

= {75($\sqrt{3}- 1$)]

Hence, the distance between the two ships is {75($\sqrt{3}- 1$)]m

Learn more: Angles of Depression

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