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

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

I think I can use the Pythagorean Theorem to solve for x, but I am not sure how to prove that the triangle is right. Since all three points do not rest on the circle.

Thank you for the help. 

Asked on by novjb

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baxthum8 | High School Teacher | (Level 3) Associate Educator

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You can use the pythagorean theorem to solve for the distance to the horizon.  Any segment drawn from a point of tangency to the center is always perpendicular.  Therefore, connect the segment from the point of tangency to the center, this is also a radius.  Now, there is formed a right triangle in which one leg is the segment from point of tangency to center = 6371 km and the hypotenuse which is 6724 km (6371+353).

Use pythagoream theorem to find the horizon (leg) x.

`x^2 + 6371^2 = 6724^2`

` ` `x^2 = 4622535`

`x = 2150.00814` km

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