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As observed from the top of a 75 m 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, what is the distance between the two ships?

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753 m

75 (3 + 1) m

75 (3 − 1) m

70 (3 − 1) m

answer is C.

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Detailed Solution

Given that,
Angle of depression from the top of the lighthouse of the ship

= 30 o

,
Angle of depression from the top of the lighthouse of the ship

= 45 o

.
Also, height of the lighthouse = 75 m.
The given situation is represented diagrammatically below,
Question Image

Δ B C A,

tan 45 = A B B C ⇒ 1 = 75 B C ⇒ B C = 75

Δ B D A,

tan 30 = A B B D ⇒ 13 = 75 B D ⇒ B D = 753

The distance between the ships = BD – BC = CD.

C D = 753 − 75 ⇒ C D = 75 (3 − 1) m

.
Therefore, the distance between the ships is

75 (3 − 1) m

at the given instance.
The correct option is 3.

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