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

We can use trigonometry to solve for the angle of depression. In the right triangle formed by the satellite, the point directly below the satellite on the surface of the Earth, and the center of the Earth, the angle of depression is opposite the side adjacent to the angle.

Let x be the distance from the point directly below the satellite to the center of the Earth. Then, x + 4000 is the hypotenuse of the right triangle, and 13000 is the opposite side. We can use the tangent function to solve for the angle of depression:

tan θ = (13000) / (x + 4000)

To solve for x, we can use the Pythagorean theorem:

(x + 4000)^2 = (13000)^2 + (4000)^2

x = sqrt[(13000)^2 + (4000)^2] - 4000

x ≈ 12,042.4 miles

Substituting x into the tangent equation, we get:

tan θ = (13000) / (12042.4)

θ ≈ 76.39º

Therefore, the answer is D) 76.39º.

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