Final answer:
To find the distance between the plane at 20000 feet elevation and the airport with a 15° angle of depression, we use the tangent function of trigonometry, dividing the elevation by the tangent of the angle to obtain the ground distance.
Step-by-step explanation:
To calculate the distance between the plane flying at an elevation of 20000 feet and the airport when the angle of depression to the airport is 15°, we can use trigonometric functions. Considering the situation as a right-angled triangle, where the elevation of the plane acts as the opposite side, the distance from the plane to the airport acts as the hypotenuse, and the angle of depression is given, we will use the tangent function (tan), which relates the angle to the opposite side and the adjacent side (ground distance).
First, convert the elevation into feet to match the units:
20000 feet (elevation) = 20000 feet.
Using the formula:
tan(θ) = opposite / adjacent
Here, θ is the angle of depression, the 'opposite' is the elevation of the plane (20000 feet), and the 'adjacent' is the distance we want to find.
tan(15°) = 20000 / distance
Solving for 'distance':
distance = 20000 / tan(15°)
After calculating, we find the distance between the plane and the airport.