Question

From an h = 53 feet observation tower on the coast, a Coast Guard officer sights a boat in difficulty. The angle of depression of the boat is θ = 4 ◦ . How far (in feet) is the boat from the shoreline? Answer in units of feet.

Answer 1

To find the distance of the boat from the shoreline, we can use the tangent function with the given height of the observation tower (h) and angle of depression (θ).

Step-by-step explanation:

To find the distance of the boat from the shoreline, we can use trigonometry. Since we have the height of the observation tower (h) and the angle of depression (θ), we can use the tangent function to find the distance (d). Tan(θ) = opposite/adjacent, where the opposite side is the height of the tower and the adjacent side is the distance we want to find. Rearranging the formula, we get tan(θ) = h/d. Substituting the given values, we have tan(4°) = 53/d. Solving for d, we get d = 53/tan(4°). Using a calculator, we find that d ≈ 764.47 feet.