Solve the triangle

Question

The path of a satellite orbiting the earth causes it to pass directly over two tracking stations A and B, which are 61 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 87.7° and 84.6°, respectively. 84.6°87.7°BA NOTE: The picture is NOT drawn to scale.

How far is the satellite from station A?

distance from A = mi

How high is the satellite above the ground?

height = mi

Answer 1

a=61mi

α=180°-92.3°-84.6°=3.1°

a/sinα=b/sinβ=c/sinγ

61/.054=1127.98=b/.996; b=1122.98; =c/.9992 "c"=1127.07

station A.

side "b" of a rt triangle=height

β=180-92.3=87.7°

Because of the rt angle; b/sinβ=c which is "b" of the original (sin90=1).

b/87.7sin=1127.07; b=1126.162mi Hight