Two ships are sailing in the sea towards a lighthouse. The angles of depression of the two ships are observed as 60° and 45° respectively. If the distance between the two ships is 100 m, find the height of the lighthouse.
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Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30 degree and 45 degree respectively. If the lighthouse is 100 m high, the distance between the two ships is: 276 metre.
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Let AD be the lighthouse of height h m B and C are the position of the two ships which are on the either side of the road. The angles of depression of the ships from the
top of the light house be 60° and 45°, ie., ∠ABD = 60 and ∠ACD = 45°
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Let BD = x m and CD = y m.
In right triangle ABD, we have
In right triangle ACD, we have
Adding (i) and (ii), we get
Hence, the height of the light house = 200 m.
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