The radius of the earth is approximately 6371 km. If the international space station (ISS) is orbiting 353 km above the earth, find the distance from the ISS to the horizon (x).

(Diagram in comments)

Question

The radius of the earth is approximately 6371 km. If the international space station (ISS) is orbiting 353 km above the earth, find the distance from the ISS to the horizon (x). 

(Diagram in comments)

anonymous · Answer

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dape · Answer

If you look at the picture you see that the horizon is tangent to the circle at X, which means that a radius from the origin O to X must intersect the horizon at right angles. So we have a right angle with sides 6371 km and 6371+353 km (look at the figure). You should now be able to solve for the third side by using the pythagorean theorem.
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