Homework SourseThe 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. Those tracking stations are 49 miles apart. When the satellite is on one side of the two stations, the angle at A and B are measured to be 87 degrees and 84 degrees.
The satellite is how many miles from station A?
Solution
Angle BAC (interior) = 180 -87 = 93deg
Angle ACB = 180 - 93 -84 = 3 deg
Use sine rule to find Distance between station A and satellite = AC
AC/sin84 = AB/sin3
AC = sin84*49/sin3 = 931.13 miles
Lets find BC to find height of satellite: apply sine rule
931.13/sin84 = BC/sin93
BC = 934.975 miles
Now Right angled triangle with height h and acute angle 84 deg with hypotenuse = 934.975
So, h =934.975*sin84 = 929.85 miles
