As observed from the top of a 60-m high light-house 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 light-house, find the distance between the two ships. [Use √3 = 1.732]

Question

Philoid · Accepted Answer

Let C and D be the two ships at a distance CD from each other

⸫ tan 45° =

⇒ 1 =

⸫ BC = 60 m

⸫ tan 30° =

⇒

⸫ BD = 60 × √3 = 60 × 1.732 = 103.92 m

⸫ Distance between the ships = CD = 103.92 – 60 = 43.92 m