Answer :

Let CD be a lighthouse such that CD = 75 m

And A and B be two ships with A directly behind B on same side of lighthouse.

To find distance between two ships = AB

Now,

Angle of depression for ship A, θ_{1} = 30°

Angle of depression for ship B, θ_{2} = 45°

Also,

∠CAD = θ_{1} = 30° [Alternate Angles]

∠CBD = θ_{2} = 45° [Alternate Angles]

Now, In ΔACD

⇒ AC = 75√3 m

In ΔBCD

⇒ BC = 75 m

Therefore,

AB = AC - BC

= 75√3 - 75

= 75(√3 - 1) m

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