Question

Qasim spots an airplane on radar that is currently approaching in a straight line, and that will fly directly overhead. The plane maintains a constant altitude of 7200 feet. Anna initially measures an angle of elevation of 16° to the plane at point A. At some later time, she measures an angle of elevation of 38° to the plane at point B. Find the distance the plane traveled from point A to point B.

Answer 1

To find the distance the plane traveled from point A to point B, one must calculate the distance from Anna to the plane for each measured angle of elevation using the tangent function and then subtract the shorter distance from the longer to get the distance traveled.

Step-by-step explanation:

The problem described is a trigonometry problem that requires the use of right triangle relationships to determine the distance a plane traveled between two points where different angles of elevation were measured. Anna initially measures an angle of elevation of 16° to the plane at point A and later measures an angle of elevation of 38° at point B. Knowing that the plane maintains a constant altitude of 7200 feet, we can use the tangent function of each angle to find the distance from Anna to the plane at each measurement.

To find the distance traveled by the plane from A to B, we need to:

1. Calculate the distance from Anna to the plane at point A using the formula distance A = altitude / tan(16°).
2. Calculate the distance from Anna to the plane at point B using the formula distance B = altitude / tan(38°).
3. Subtract the distance at point A from the distance at point B to find the distance the plane traveled.

Using a calculator with the tangent function:

• distance A = 7200 / tan(16°)
• distance B = 7200 / tan(38°)

Then, the distance the plane traveled from A to B = distance B - distance A.