A boat is heading towards a lighthouse, whose beacon-light is 140 feet above the water. The boat’s crew measures the angle of elevation to the beacon, 10degrees ∘ . What is the ship’s horizontal distance from the lighthouse (and the shore)? Round your answer to the nearest tenth of a foot if necessary.
Question
A boat is heading towards a lighthouse, whose beacon-light is 140 feet above the water. The boat’s crew measures the angle of elevation to the beacon, 10degrees ∘ . What is the ship’s horizontal distance from the lighthouse (and the shore)? Round your answer to the nearest tenth of a foot if necessary.
Solution
To solve this problem, we can use the tangent of the angle of elevation, which is the ratio of the opposite side (height of the lighthouse) to the adjacent side (distance from the lighthouse).
The formula for tangent is:
tan(θ) = opposite/adjacent
We know the opposite side (height of the lighthouse) is 140 feet and the angle of elevation (θ) is 10 degrees. We want to find the adjacent side (distance from the lighthouse).
Rearranging the formula to solve for the adjacent side gives us:
adjacent = opposite/tan(θ)
Substituting the given values into the formula gives us:
adjacent = 140/tan(10)
Using a calculator to find the tangent of 10 degrees and then divide 140 by that number gives us the distance from the lighthouse.
Remember to round your answer to the nearest tenth of a foot if necessary.
Similar Questions
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