Final answer:
To find the average angle of descent for an airplane, convert the distance to the same units as altitude, create a right triangle, and use the arctangent of altitude over distance to determine the angle, rounding to the nearest degree.
Step-by-step explanation:
The student is asking about finding the average angle of descent for an airplane preparing to land. The airplane is currently at 10,000 feet altitude and needs to land at an airport that is 50 miles away. To solve this problem, we can visualize it as a right triangle where the altitude is one leg, the distance to the airport is the other leg, and the angle of descent is the angle we wish to find.
First, we must convert the distance from miles to feet to match the units of altitude: 1 mile = 5,280 feet, so 50 miles = 50 * 5,280 = 264,000 feet. Now we can use trigonometry, specifically the tangent function, which is the ratio of the opposite side over the adjacent side in a right triangle. The formula will be tangent(angle) = opposite/adjacent, or in our case, tangent(angle) = 10,000/264,000.
Using a calculator, we find the angle by calculating the arctangent (also known as the inverse tangent) of 10,000/264,000, which gives us the angle in degrees when we round to the nearest degree.