SOLUTION: Suppose a space shuttle is orbiting about 180 miles above Earth. What is the distance from the shuttle to the horizon? The radius of Earth is about 4000 miles. Round the answer to

Question 292714: Suppose a space shuttle is orbiting about 180 miles above Earth. What is the distance from the shuttle to the horizon? The radius of Earth is about 4000 miles. Round the answer to the nearest tenth.
Answer by dabanfield(803) (Show Source): You can put this solution on YOUR website!
The shuttle, the point on the horizon and the center of the earth create a right triangle with right angle where the radius intersects the tangent line from the shuttle to the horizon. The radius is 4000 and the hypotenuse from the center of the earth to the shuttle is 4000+180. Let d be the distance from the shuttle to the horizon. By the Pythagorean Theorem we have then:
4180^2 = 4000^2 + d^2
d^2 = 4180^2 - 4000^2
Solve for d.
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