Final answer:
To find the distances in question, trigonometry is used. The angle of depression gives the tangent of the angle to find the horizontal distance, and the Pythagorean theorem gives the straight-line distance to the airport.
Step-by-step explanation:
The subject question requires the use of trigonometry to find the distance between the airplane and the airport and between the point on the ground directly below the plane and the airport. When the angle of depression to the airport is 16°, and the plane is at a height of 30000 feet, we can use tangent because it involves an angle with the opposite side (height) and the adjacent side (ground distance to the airport) of a right triangle.
Let's represent the distance between the plane and the airport as d and the distance on the ground directly below the plane to the airport as x. Since the angle of depression from the plane to the airport is the same as the angle of elevation from the ground to the plane (alternate interior angles), we can set up the following equation using the tangent:
tan(16°) = opposite/adjacent = 30000 feet / x
By solving for x, we find:
x = 30000 feet / tan(16°)
Once x is calculated, we can use the Pythagorean theorem to find the straight-line distance d (hypotenuse) between the plane and the airport:
d = sqrt(30000^2 + x^2)
Note that in these calculations, it's important to ensure your calculator is set to the correct unit (degrees in this case) for trigonometric functions.