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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 84 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 = 84 metres [Given]
The point 'C' be the position of the ship,
∴ ∠ ACB = 60°
`tan 60° = ("Opposite side of "60°) /("Adjacent side of "60°)`
∴ `tan 60° = "AB" / "BC"`
∴ `sqrt3 = 84/"BC"`
∴ `"BC" = 84/sqrt3`
∴ `"BC" = (84/sqrt3)×sqrt3/sqrt3`
∴ BC = 28√3
∴ BC = 28× 1.73
∴ BC = 48.4 m.
∴ The ship is 48.4 m away from the lighthouse.
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