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)
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! 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
|
|
|
