Final answer:
To find the angle of depression from a lighthouse to a boat, use inverse tangent with the lighthouse's height as the opposite side and the distance to the boat as the adjacent side of the right-angled triangle.
Step-by-step explanation:
To calculate the angle of depression from the top of a 27-meter-tall lighthouse to a boat that is 98.7 meters away, you can use trigonometry. Specifically, the angle of depression corresponds to the angle we want to find in a right-angled triangle formed by the lighthouse, the boat, and the point directly below the lighthouse on the level of the water.
In such a triangle, the lighthouse's height forms the opposite side, the distance from the boat to the point directly under the lighthouse forms the adjacent side, and the angle of depression forms the angle we want to find. Therefore, we use the tangent function (tan = opposite/adjacent), thus tan(θ) = 27/98.7. To find the angle θ in degrees, we take the inverse tangent (arctan) of (27/98.7) using a calculator.