Question

A satellite orbiting the earth uses radar to communicate with two control stations on the earths surface the satellites orbit maintains a 10 degree angle of separation between the two stations, as shown in the picture below. Knowing that earth’s radius is 3,963 miles, sender the following questions. Round all wanders to the nearest whole number

Answer 1

What is the distance between the two control stations on the earth's surface?

To find the distance between the two control stations, we can use the law of cosines. Let's call the distance between the control stations "d". Then, using the information that the angle of separation between the two stations is 10°:

d^2 = 2 * 3963^2 - 2 * 3963^2 * cos(10°)

d = sqrt(2 * 3963^2 - 2 * 3963^2 * cos(10°))

Using a calculator, we find that d = approximately 5657 miles. Rounding to the nearest whole number, the distance between the two control stations is 5657 miles.

What is the height of the satellite above the surface of the earth?

To find the height of the satellite, we can use the law of sines. Let's call the height of the satellite "h". Then, using the information that the distance between the two control stations is d:

h / sin(10°) = d / 2

h = d / 2 * sin(10°)

Using the value of d from the previous question, and a calculator, we find that h = approximately 22,795 miles. Rounding to the nearest whole number, the height of the satellite above the surface of the earth is 22,795 miles.

Explanation: