Solve the problem.
-A rocket tracking station has two telescopes A and B placed 2.1 miles apart. The telescopes lock onto a rocket and transmit their angles of elevation to a computer after a rocket launch. What is the
Distance to the rocket from telescope B at the moment when both tracking stations are directly east
Of the rocket telescope A reports an angle of elevation of 20° and telescope B reports an angle of
Elevation of 52°? Round to the nearest hundredth of a mile.
A) 0.91 mi
B) 1.36 mi
C) 4.84 mi
D) 3.12 mi

Question

Quizplus · Accepted Answer

To solve this problem, we can use trigonometry, specifically the tangent of the angles of elevation. Let $ x $ be the distance from telescope B to the rocket. The distance from telescope A to the rocket is $ x + 2.1 $ miles because A and B are 2.1 miles apart. Using the tangent of the angles, we have:For telescope A (20°): $\tan(20°) = \frac{height}{x + 2.1}$For telescope B (52°): $\tan(52°) = \frac{height}{x}$Since the height of the rocket is the same in both equations, we can set them equal to each other and solve for $ x $:$\frac{\tan(52°)}{\tan(20°)} = \frac{x + 2.1}{x}$Solving this equation gives $ x \approx 1.36 $ miles, which is the distance from telescope B to the rocket.

Solve the Problem. -A Rocket Tracking Station Has Two Telescopes a and B