From the top of a lighthouse which is 90 m above the sea, the angle of depression of a ship is 60°. How far is the ship from the lighthouse? 

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  1. 30√3 m
  2. 30 m
  3. 17.34 m
  4. 20.5 m

Answer (Detailed Solution Below)

Option 1 : 30√3 m
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Detailed Solution

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Given:

A lighthouse is 90 m above the sea, and the angle of depression to a ship is 60º.

Concept:

In a right triangle, the tangent of the angle of depression equals the ratio of the opposite side (height of the lighthouse) to the adjacent side (distance of the ship from the lighthouse).

Formula Used:

tan(θ) = opposite / adjacent

Calculation:

We have,

⇒ tan(60º) = 90 m / distance

We know, tan(60º) = √3

⇒ √3 = 90 m / distance

⇒ distance = 90 m / √3

⇒ distance = 90 m / (√3 / 3)

⇒ distance = 90 m × (3 / √3)

⇒ distance = 30√3 m

∴ The distance of the ship from the lighthouse is 30√3 m.

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