# As observed from the top of a lighthouse, 200 m above the sea level, the angle of depression of a ship sailing towards it changes from 30° to 45°. Determine the distance travelled by the ship during the period of observation.

To find:

The distance travelled by ship.

Formula Used:

Explanation:

Let A and B be two positions of the ship.

Let d be the distance travelled by the ship i.e. AB = d metres

PO = 200 metres

OAP = 30° and OBP = 45°

In Δ OPB,

BP = 200 m

In ΔOPA,

d + BP = 200√3

d + 200 = 200√3

d = 200√3 – 200

d = 200(√3 – 1)

d = 200(1.732 – 1)

d = 146.4 m

Hence distance travelled by ship is 146.4 m.

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