Sailors on a ship at sea spot the light from a lighthouse at an angle of elevation of 25°. The light of the lighthouse is 30 meters above sea level. How far from shore is the ship? Round your answer to the nearest meter.

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Answer:

The ship is approximately 14 meters from shore

Step-by-step explanation:

Let the distance between the ship and the lighthouse be x

From the diagram:

Tan (25) = [tex]\frac{Opposite}{Adjacent} = \frac{30}{x}[/tex]

0.466 = [tex]\frac{30}{x}[/tex]

∴ [tex]x[/tex] = 30× 0.466 = 13.98 = 14 m ( to the nearest meter)

Therefore, the ship is 14 meters from shore

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