fatoumata spots an airplane on radar that is currently approaching in a straight line, and that will fly…

fatoumata 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 6875 feet. fatoumata initially measures an angle of elevation of 17° to the plane at point a. at some later time, she measures an angle of elevation of 40° 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.

fatoumata 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 6875 feet. fatoumata initially measures an angle of elevation of 17° to the plane at point a. at some later time, she measures an angle of elevation of 40° 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

Explanation:

Step1: Use the tangent function for both angles

Let the horizontal distance from the point directly below the plane to point (A) be (x_1) and to point (B) be (x_2). We know that (\tan\theta=\frac{\text{opposite}}{\text{adjacent}}). For the initial angle of elevation (\theta_1 = 17^{\circ}), (\tan(17^{\circ})=\frac{6875}{x_1}), so (x_1=\frac{6875}{\tan(17^{\circ})}). For the later angle of elevation (\theta_2 = 40^{\circ}), (\tan(40^{\circ})=\frac{6875}{x_2}), so (x_2=\frac{6875}{\tan(40^{\circ})}).

Step2: Calculate the distance traveled (d)

The distance traveled (d=x_1 - x_2). We know that (\tan(17^{\circ})\approx0.3057) and (\tan(40^{\circ})\approx0.8391). (x_1=\frac{6875}{0.3057}\approx22500) (x_2=\frac{6875}{0.8391}\approx8200) (d = 22500-8200=14300)

Answer:

(14300) feet