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From the top of a lighthouse, an observer looks at a ship and find the angle of depression to be 60º. If the height of the lighthouse is 90 metres then find how far is that ship from the lighthouse ? ( √3 = 1.73)

2. From the top of a lighthouse, an observer looks at a ship and find the angle of depression to be 60º. If the height of the lighthouse is 90 metres then find how far is that ship from the lighthouse ? ( √3 = 1.73)

Sol.



Let AB be the height of the lighthouse,
∴ AB = 90 metres [Given]
The point 'C' be the position of the ship,
∴ ∠ ACB = 600
tan 600 = Opposite side of 600 / Adjacent side of 600
∴ tan 600 = AB / BC
∴ √3 = 90/BC
∴ BC = 90/√ 3
∴ BC = (90/√3)× √3/√3
∴ BC =  30√3
∴ BC = 30× 1.73
∴ BC = 51.9 m.

∴ The ship is 51.9 m away from the lighthouse.