Final answer:
To calculate the angle of depression from an airplane to an airport, use the tangent function. The angle is approximately 4.42 degrees, which doesn't match the provided choices; there may be an error in the question's provided data or choices.
Step-by-step explanation:
The student's question involves calculating the angle of depression from an airplane to an airport. To find the angle of depression, we can use trigonometry, specifically the tangent function, since the angle regards the plane's altitude and horizontal distance to the airport as a right triangle.
To find the angle of depression θ, we know from trigonometry that:
tan(θ) = opposite/adjacent
where the opposite side is the airplane's altitude (7 miles) and the adjacent side is the distance from the airplane to the airport (165 miles). So,
tan(θ) = 7/165
Using a calculator, we find that:
θ = tan⁻¹(7/165)≈ 4.42°
Therefore, the angle of depression from the airplane to the airport is approximately 4.42°, which is not one of the provided options in the multiple-choice question. The student may need to recheck the given distances or the possible answer choices for errors.