Posted by **Ariel** on Monday, March 19, 2012 at 8:13pm.

11-1 Lines that Intersect Circles

8. The International Space Station orbits Earth at an altitude of 240 miles. What is the distance from the space station to Earth's horizon to the nearest mile?

- Geometry -
**Steve**, Monday, March 19, 2012 at 11:56pm
radius of earth: 6378

radius of orbit: 6618

draw a right triangle with legs 6378 and d, and hypotenuse 6618

6378^2 + d^2 = 6618^2

d^2 = 3119040

d = 1766 mi

- Geometry -
**Peter**, Monday, April 23, 2012 at 10:38am
Sorry Steve, you made a major error with your units... the radius of the Earth is around 6378 km not 6378 miles.

You are trying to find the distance from the Space Station to the horizon, which would be the point of tangency. The tangent line from the Space Station will form a right angle with the center of the Earth. The radius of the Earth is 4000 miles, and the distance from the center of the earth to the Space Station is 4240 miles from the center of the Earth (radius + altitude).

Use Pythagorean Theorem:

radius of Earth squared + distance to horizon squared = distance from center of earth to Space Station squared.

4000^2 + x^2 = 4240^2

x^2 = 1977600

x = 1406.27

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