Question

zahra 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 7375 feet. zahra initially measures an angle of elevation of 16° to the plane at point a. at some later time, she measures an angle of elevation of 34° 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.

Explanation:

Step1: Define variables

Let $x$ = horizontal distance to A, $y$ = horizontal distance to B.

Step2: Calculate $x$

$\tan(16^\circ)=\frac{7375}{x} \Rightarrow x=\frac{7375}{\tan(16^\circ)}$
$x\approx\frac{7375}{0.2867}\approx25723.7$

Step3: Calculate $y$

$\tan(34^\circ)=\frac{7375}{y} \Rightarrow y=\frac{7375}{\tan(34^\circ)}$
$y\approx\frac{7375}{0.6745}\approx10931.5$

Step4: Find distance AB

$AB=x-y\approx25723.7-10931.5=15012.2$

Answer:

15012.2 feet