Question 1043922: The path of a satellite orbiting the earth causes it to pass directly over two tracking stations A and B, which are 50 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.
(a) How far is the satellite from station A?
(b) How high is the satellite above the ground?
Found 2 solutions by josgarithmetic, hahamaster:
Answer by josgarithmetic(39617)   (Show Source):
You can put this solution on YOUR website! Make this drawing described:
Horizontal segment BA, point S slightly to the right of A and above it.
Interior angle at B is 84 degrees; interior angle at A is 87 degrees. Segment BA is 50 miles.
Sum of interior angles of triangle BAS will give measure of interior angle at S is 9 degrees.
One of the questions means, find measure of AS. This can be done using Law Of Sines.
Solve this for the value of measure of AS.
Distance from S to LINE BA is a little more complicated.
Start by extending the segment from point A along line BA; draw perpendicular segment from S to line BA. You want this distance. Call this some variable, maybe, y.
You now have a smaller, RIGHT Triangle of sides AS (which you found now), height y, new angle at angle A being 93 degrees; and you want to solve for y. Understand too, AS is hypotenuse, and is opposite a right angle.
-
 (although not the only way...)
 , which you can simplify and compute.
Answer by hahamaster(1) (Show Source):
|
|
|
