Question

13. Gavin 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 6050 feet. Gavin initially measures an angle of elevation of 16° to the plane at point A. At some later time, he measures an angle of elevation of 37° to the plane at point B. Find the distance the plane traveled from point A to point B. Round your answer to the nearest foot if necessary.​

Answer 1

Answer: Let's denote the distance the plane travels from point A to point B by d. We can then use trigonometry to set up two equations based on the angles of elevation and the constant altitude of the plane:

At point A:

tan(16°) = 6050 / x, where x is the distance between Gavin and the point directly beneath the plane at point A.

At point B:

tan(37°) = 6050 / (x + d), where x + d is the distance between Gavin and the point directly beneath the plane at point B.

We can solve for x in the first equation:

x = 6050 / tan(16°) ≈ 20416.6 ft

Substituting this into the second equation and solving for d, we get:

d = (6050 / tan(37°)) - x ≈ 22451.4 ft

Therefore, the distance the plane traveled from point A to point B is approximately 22,451 feet (rounded to the nearest foot).

Explanation: