Question

An observer (O) spots a plane (P) taking off from a local airport and flying at a 23° angle horizontal to her line of sight and located directly above a bird (B) circling directly above her. If the distance from the plane (P) to the tower (T) is 5,000 ft., how far is the bird (B) from the plane (P)?

a) 5429 feet
b) 5000 feet
c) 23 feet
d) 32.84928 feet

Answer 1

To determine the distance between the bird and the plane, we can use trigonometry. The bird is approximately 5,429 feet from the plane.

Step-by-step explanation:

To determine the distance between the bird and the plane, we can use trigonometry. Let's consider the right triangle formed by the observer (O), the bird (B), and the plane (P). The angle between the line of sight from the observer to the bird and the horizontal is 23°.

We know the distance from the plane to the tower (T) is 5,000 ft. Let x be the distance between the bird and the plane. Using trigonometry, we can set up the equation: tan(23°) = x/5000. Solving for x, we find that the bird is approximately 5,429 feet from the plane.