Question 720002
The path of a satellite orbiting the earth causes it to pass directly over two tracking stations A and B, which are 55 miles 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 degrees and 84 degrees, respectively. 
How far is the satellite from station A? 
How high is the satellite above ground? 
(both answers in miles)
***
let h=distance satellite is above ground
let x=distance from point on ground directly below satellite to tracking stations on the ground
let s=distance satellite from station A 
h/x=tan 87º
h/(55+x)=tan 84º
..
h=x tan87º
h=(55+x)tan 84º
..
xtan87º=(55+x)tan84º
19.08x=523.29+9.51x
9.57x=523.29
x=54.68
h=54.68*tan87≈1043 mi
sin 87º=h/s
s=h/sin 87≈1044 mi
distance satellite is above ground≈1043 mi
distance satellite from station A ≈1044 mi