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in Trigonometry by (56.3k points)

As observed from the top of a 75 m tall lighthouse, 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.

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Given;

Height of the lighthouse = 75 m = ‘h’ m = AB

Angle of depression of ship 1, α = 30°

Angle of depression of bottom of the tall building, β = 45°

The above data is represented in form of figure as shown

Let distance between ships be ‘x’ m = CD

If in right angle triangle one of the included angle is θ

Therefore, the distance from the ships is 75(√3 + 1) m.

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