Question

kayden 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 5875 feet. kayden initially measures an angle of elevation of $16^\circ$ to the plane at point $a$. at some later time, he measures an angle of elevation of $33^\circ$ to the plane at point $b$. find the distance the plane traveled from point $a$ to point $b$. round your answer to the nearest tenth of a foot if necessary.
answer attempt 1 out of 2
feet

Explanation:

Step1: Find horizontal distance to A

Let $x_A$ = horizontal distance to A.
$\tan(16^\circ) = \frac{5875}{x_A} \implies x_A = \frac{5875}{\tan(16^\circ)}$
$x_A \approx \frac{5875}{0.2867} \approx 20491.8$ feet

Step2: Find horizontal distance to B

Let $x_B$ = horizontal distance to B.
$\tan(33^\circ) = \frac{5875}{x_B} \implies x_B = \frac{5875}{\tan(33^\circ)}$
$x_B \approx \frac{5875}{0.6494} \approx 9046.2$ feet

Step3: Calculate distance AB

Distance $AB = x_A - x_B$
$AB \approx 20491.8 - 9046.2 = 12322.6$ feet

Answer:

12322.6 feet