Question

A boat is heading towards a lighthouse, whose beacon-light is 126 feet above the water. The boat’s crew measures the angle of elevation to the beacon, 13∘. 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

Answer 1

To calculate the horizontal distance from the lighthouse, use the tangent function with the angle of elevation at 13° and the height of the beacon at 126 feet, then solve for the adjacent side of the right triangle.

Step-by-step explanation:

The student's question pertains to finding the horizontal distance from a boat to a lighthouse when the angle of elevation to the beacon is given. To solve this problem, one can use trigonometric functions, specifically the tangent function which relates the angle of elevation to the opposite and adjacent sides of a right triangle. The opposite side here is the height of the lighthouse's beacon above water, and the adjacent side will be the horizontal distance we want to calculate.