A boat is heading towards a lighthouse, whose beacon-light is 139 feet above the water. The
boat's crew measures the angle of elevation to the beacon, 5°. 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.
Let's set up a right triangle to represent the situation.
The lighthouse is at the top of the triangle, the boat is at the bottom, and the horizontal distance from the boat to the lighthouse is the hypotenuse of the triangle.
We know that the angle of elevation from the boat to the beacon is 5°, and the height of the beacon is 139 feet.
Using trigonometry, we can use the tangent function to find the length of the hypotenuse.
tan(5°) = (opposite)/(adjacent)
tan(5°) = 139/(adjacent)
To solve for the adjacent side (which is the horizontal distance from the boat to the lighthouse), we can rearrange the equation:
adjacent = 139/tan(5°)
Now we can calculate the value:
adjacent = 139/tan(5°) ≈ 1585.43 feet
Therefore, the ship's horizontal distance from the lighthouse is approximately 1585.43 feet.