Question

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.

You will use the GeoGebra geometry tool to model and solve this problem. Open GeoGebra, and complete each step below. If you need help, follow these instructions for using GeoGebra.

Part A

To achieve maximum coverage of the signal across Earth, what type of line should be formed between the point where the satellite is located and the point on Earth’s surface where the signal is received?

Part B

Create a cross-sectional diagram of this situation in GeoGebra, with the circumference of Earth depicted as a circle (your diagram need not be drawn to scale):

Create point C for the center of Earth, point S for the position of the satellite, and points P1 and P2 for the farthest points on Earth where the signal will reach.
Draw a radius from C to P1 and a line segment from S to P1. Display the measure of the angle formed at their intersection. In the space provided below, note how CP¯1 and SP¯1 are related.
Use the Internet or another resource to find the approximate radius of Earth, and note it in the space provided below. Then label the lengths of CP¯1 and SP¯1.
Take a screenshot of your work, save it, and insert the image below your answers.

Part C

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.

please some answer me asap

Answer 1

To achieve maximum coverage of the signal, a line of sight should be formed between the satellite and the point on Earth's surface. By creating a cross-sectional diagram in GeoGebra, you can measure the angle formed and determine the height of the satellite above the surface. The optimal height for maximum coverage is equal to the sum of the radius of Earth and the height measured from the diagram.

Step-by-step explanation:

In order to achieve maximum coverage of the signal across Earth, a line of sight should be formed between the point where the satellite is located and the point on Earth's surface where the signal is received.

To determine the optimal height for the satellite, you can create a cross-sectional diagram in GeoGebra. Label the center of Earth as point C, the position of the satellite as point S, and the farthest points on Earth where the signal will reach as points P1 and P2. Draw a radius from C to P1 and a line segment from S to P1. Measure and record the angle formed at their intersection. CP¯1 represents the radius of Earth, while SP¯1 represents the height of the satellite above the surface of Earth.

The distance that the satellite needs to be above the surface of Earth to provide maximum coverage of its signal is equal to the radius of Earth plus the height at which the satellite is located. By adding the approximate radius of Earth to the height, you can determine the required distance above the surface.