A communications company is planning to launch a new satellite into orbit to improve the operation of its network. The longest distance that the satellite can send a reliable signal is 4,500 miles. The company is trying to determine the optimal height to operate the satellite so that it has maximum coverage of Earth within its range.

Question: With the satellite directly overhead, how far above the surface of Earth does the satellite need to be so it provides the maximum coverage of its signal? Explain how you arrived at the answer.