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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.

please helpppp A communications satellite is in a synchronous orbit 22000 miles above Earths surface Points B and D in the figure are points of tangency of the class=

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sqdancefan

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Answer:

  1. 25,690 mi
  2. 45%

Step-by-step 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.

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