Pre-cal...??

Question

A satellite, S, in circular orbit around the Earth is sighted by a tracking station T. The distance TS is determined by radar to be 1,034 miles, and the angle of elevation above the horizon is 32.4 degrees. how high is the satellite above the earth at the time of the sighting. radius of earth= 3.914.189 miles.

Answer 1

Oooh, that is an interesting one! I'll have to think about it.
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OK, I thought about it and got 638.5359 miles. I drew a triangle with one corner at the center of the Earth, one at the tracking station and one at the satellite. You know the length of two sides from the problem statement and the third side, the long one, is the altitude plus the radius of the Earth. The obtuse angle at the tracking station is 32.4+90=122.4 degrees because the horizon line is tangent to the Earth at the tracking station and so at right angles to the line from the tracking station to the center of the Earth; and the satellite is seen 32.4 degrees above that line. Then I used the law of cosines (see the source) to solve for the distance from the center of the Earth to the satellite and subtracted the radius of the Earth to get the altitude.