The path of a satellite orbiting the earth causes it to pass

The path of a satellite orbiting the earth causes it to pass directly over two tracking stations A and B, which are 35 mi apart. When the satellite is on one side of the two stations, the angles of elevation at A and B are measured to be 87.0° and 84.2°, respectively. (Round your answers to the nearest mile.) (a) How far is the satellite from station A? mi (b) How high is the satellite above the ground? mi

Solution

h=distance satellite is above ground

x=distance from point on ground directly below satellite to tracking stations on the ground

s=distance satellite from station A

h/x = tan 87

h/(35 + x) = tan 84.2

x*tan 87 = (35+x)*tan 84.2

x = 35*tan 84.2/(tan 87 - tan 84.2)

x = 37.30 mi

h = 37.30*tan 87 deg = 711.73 miles = 712 miles

sin 87 = h/s

s = 711.73/sin 87 deg = 712.71 miles = 713 miles