A boat is heading towards a lighthouse, whose beacon-light is 113 feet above the water. The boat’s crew measures the angle of elevation to the beacon, 7degrees
∘
. 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.
To find the horizontal distance from the boat to the lighthouse, we can use the tangent function in trigonometry.
tan(theta) = opposite/adjacent
Let x be the horizontal distance from the boat to the lighthouse. The opposite side is the height of the beacon, which is 113 feet. The angle of elevation is 7 degrees.
tan(7 degrees) = 113 feet / x
x = 113 feet / tan(7 degrees)
x ≈ 113 feet / 0.122738
x ≈ 920.3 feet
Therefore, the boat is approximately 920.3 feet away from the lighthouse.