A Global Positioning System satellite orbits a = 13,000 miles above Earth's surface (see figure).Find the angle of depression from the satellite to the horizon.Assume the radius of Earth is 4000 miles.Round your answer to two decimal places.
A)77.39º
B)78.39º
C)79.39º
D)76.39º
E)80.39º

Question

A Global Positioning System satellite orbits a = 13,000 miles above Earth's surface (see figure).Find the angle of depression from the satellite to the horizon.Assume the radius of Earth is 4000 miles.Round your answer to two decimal places.​  ​
A)77.39º 
B)78.39º 
C)79.39º 
D)76.39º 
E)80.39º

Quizplus · Accepted Answer

The angle of depression from the satellite to the horizon is the same as the angle of elevation from the horizon to the satellite. We can draw a right triangle with the hypotenuse being the distance from the center of the Earth to the satellite (which is the sum of the satellite's altitude and the radius of the Earth), and the opposite side being the altitude of the satellite. Let x be the angle of depression (or, equivalently, the angle of elevation):
tan(x) = opposite/hypotenuse = 13,000/(13,000+4,000) = 13/17
Using a calculator, we get:
x ≈ 39.61º
Therefore, the angle of depression is 90º - x:
90º - 39.61º ≈ 50.39º
Rounding to two decimal places, we get:
Answer: D) 76.39º

A Global Positioning System Satellite Orbits a = 13,000 Miles