Question

Anna 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 7025 feet. anna initially measures an angle of elevation of 15degrees ∘ to the plane at point aa. at some later time, she measures an angle of elevation of 25degrees ∘ to the plane at point bb. find the distance the plane traveled from point aa to point bb. round your answer to the nearest tenth of a foot if necessary.

Answer 1

The distance the plane traveled from point aa to point bb is approximately 2557.3 feet.

Step-by-step explanation:

To find the distance the plane traveled from point aa to point bb, we can use trigonometry. Let's assume the distance the plane traveled is d feet. We can create a right triangle, where the height is the constant altitude of the plane (7025 feet) and the base is the distance the plane traveled (d feet). From point aa, we have an angle of elevation of 15 degrees, which means that we can use the tangent function: tan(15) = height/base. Similarly, from point bb, we have an angle of elevation of 25 degrees: tan(25) = height/(base + d).

Now, we can solve these two equations simultaneously to find the value of d. Rearranging the equations, we get:

d = height * tan(25) - base * tan(15) = 7025 * tan(25) - 7025 * tan(15) = 2557.3 feet.

Therefore, the distance the plane traveled from point aa to point bb is approximately 2557.3 feet.