space science

[precalhelp]

a satellite S, in circular orbit around the earth, is sighted by a tracking section T. The distance TS is determined by radar to be 1,034 miles, and the angle of elevation above the horizon is 32.4degrees. How high is the satellite above the earth at the time of the sighting? The radius of the earth is 3,964 miles.

 

[TchrWill]

a satellite S, in circular orbit around the earth, is sighted by a tracking section T. The distance TS is determined by radar to be 1,034 miles, and the angle of elevation above the horizon is 32.4degrees. How high is the satellite above the earth?

Draw yourself 2 circles and display the given information.
S = satellite
T = tracking station
Call the center of the earth E.
Draw triangle TSE.
Angle STE = 122.4º
TS = 1034 miles
TE = 3964 miles
Call the satellite radius from the earth"s center SE = R.
Using the Law of Cosines, R^2 = 1034^2 + 3964^2 - 2(1034)(3964)cos(122.4º).
Solve for R.
Having R, subtract the earth's radius and t you have the distance of the satellite above the earth.