Question

question
jevonte 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 5550 feet. jevonte initially measures an angle of elevation of $15^\circ$ to the plane at point $a$. at some later time, he measures an angle of elevation of $30^\circ$ 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

Explanation:

Step1: Find horizontal distance to A

Let $x_A$ = horizontal distance from observer to point below A. Use $\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$:
$\tan(15^\circ)=\frac{5550}{x_A}$
$x_A=\frac{5550}{\tan(15^\circ)}$
$x_A\approx\frac{5550}{0.2679}\approx20716.7$ feet

Step2: Find horizontal distance to B

Let $x_B$ = horizontal distance from observer to point below B.
$\tan(30^\circ)=\frac{5550}{x_B}$
$x_B=\frac{5550}{\tan(30^\circ)}$
$x_B\approx\frac{5550}{0.5774}\approx9612.6$ feet

Step3: Calculate distance AB

AB = $x_A - x_B$
$AB\approx20716.7 - 9612.6=10168.1$ feet

Answer:

10168.1 feet