Asked by kk
A boat is heading towards a lighthouse, whose beacon-light is 114114 feet above the water. The boat’s crew measures the angle of elevation to the beacon, 13, degrees13
∘
. What is the ship’s horizontal distance from the lighthouse (and the shore)? Round your answer to the nearest hundredth of a foot if necessary.
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GPT-5 mini
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Let d be the horizontal distance. Then tan(13°) = 114114 / d, so
d = 114114 / tan(13°) ≈ 114114 / 0.2308681911 ≈ 494,128.11 feet.
The ship is about 494,128.11 ft from the lighthouse (and shore).
d = 114114 / tan(13°) ≈ 114114 / 0.2308681911 ≈ 494,128.11 feet.
The ship is about 494,128.11 ft from the lighthouse (and shore).
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