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A ship is sailing toward a 50m tall lighthouse. The angle of elevation from the ship to the top of the tower is 20°. How far is the ship from the lighthouse?

User Andyrooger
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Final answer:

To find the distance of the ship from the lighthouse, the tangent of the angle of elevation (20°) is equal to the height of the lighthouse (50m) divided by the distance. By solving the equation, we get the ship's distance from the lighthouse.

Step-by-step explanation:

To determine how far the ship is from the lighthouse, we can use trigonometric functions, specifically the tangent function. The angle of elevation is given as 20°, and the height of the lighthouse is 50m.

To find the distance (d) from the ship to the lighthouse, we can set up the following equation based on the tangent of the angle:

tan(20°) = opposite/adjacent which is tan(20°) = 50m/d.

By solving this equation for d, we get:

d = 50m / tan(20°)

After calculating this using a calculator, we find the distance d.

User Simeon Leyzerzon
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