Q13 of 34 Page 1

From the top of a lighthouse 75 m high, the angles of depression of two ships are observed to be 30ᵒ and 45ᵒ respectively. If one ship is directly behind the other on the same side of the lighthouse then find the distance between the two ships.


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, θ1 = 30°


Angle of depression for ship B, θ2 = 45°


Also,


∠CAD = θ1 = 30° [Alternate Angles]


∠CBD = θ2 = 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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