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The radius of the earth is approximately 6371km.If the international space station...

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novjb | Salutatorian

Posted September 8, 2013 at 10:34 PM via web

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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. 

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

Posted September 8, 2013 at 11:43 PM (Answer #1)

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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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