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As observed from the top of a lighthouse, 100 metres high above sea level, the angle of depression of a ship moving directly towards it, changes from 30o to 60o. Determine the distance travelled by the ship during the period of observation.

Asked by Topperlearning User 27th July 2017, 11:02 AM
Answered by Expert

Let A and B be the two positions of the ship. Let d be the distance travelled by the ship during the period of observation, i.e., AB=d metres.

Suppose that the observer is at the point P. It is given that PC = 100m.

Let h be the distance (in metres) from B to C.

In right triangle PCA,

= cot30o =

d+h = 100 ... (i)

In triangle PCB,

= cot60o =

h = metres

Putting the value of h in (i), we get,

d= 100(approx.)

Thus, the distance travelled by the ship from A to B is 115.47 metres (approx.).

Answered by Expert 27th July 2017, 1:02 PM
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