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Question
From the top of a lighthouse, an observer looks at a ship and finds the angle of depression to be 60° . If the height of the lighthouse is 90 meters, then find how far is that ship from the lighthouse? (√3 = 1.73)
Solution
As shown in the figure, assume AB as the lighthouse and let A be the position of the observer and C be the position of the ship. Let the distance from the ship to the lighthouse be x.
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.
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