Q. 184.0( 4 Votes )

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.

Answer :

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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