Question

Please helpppp

A communications satellite is in a synchronous orbit 22,000 miles above Earth’s surface. Points B and D in the figure are points of tangency of the satellite signal with the Earth. They represent the greatest distance from the satellite at which the signal can be received directly. Point C is the center of the Earth.

1. Find distance LaTeX: \overline{AB}
A B ¯ . Round to the nearest mile. Show your process and explain your reasoning.

2. m∠BAC = 9°. If the circumference of the circle represents the Earth’s equator, what percent of the Earth’s equator is within range of the satellite’s signal? Show your process and explain your reasoning.

Answer 1

9514 1404 393

Answer:

1. 25,690 mi
2. 45%

Explanation:

1. The Pythagorean theorem tells you ...

AB² +BC² = AC²

AB² = AC² -BC² = 26000² -4000² = 6.6×10⁸

AB = √6.6×10⁸

AB ≈ 25,690 . . . . miles

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2. ∠ECB = 90° -9° = 81°

This angle is 81/180 = 45% of the semicircle to the left of line EC. The same percentage is covered on the other side of that line.

45% of the Earth's equator is within signal range.