Answer:
1221.967 (DISTANCE FROM SATELLITE TO A)
1220.293 miles(DISTANCE FROM SATELLITE TO GROUND)
Explanation:
Answer: So unfortunately a lot of these answers for this question are not answering it correctly for the way that it is asked in my homework, which is not their fault because they cannot see the image in which it is referring to. Thats because in this question when it says the angle of elevation of A is 87° it is actually talking about the angle OUTSIDE of side A in the image, NOT THE INSIDE ANGLE. meaning that the inside angle across from angle B at 84.2 is actually 93° not 87°. (since it is the corresponding angle on a 180° line and we follow the geometric laws).
Now say we name the triangle ABC, we now have INNER ANGLE A at 93° and INNER ANGLE B at 84.2°.
To get INNER ANGLE C you subtract both ANGLE A & B added together from 180° to get ANGLE C since the all interior angles of a triangle = 180°
180°-(93°+84.2°)=2.8° so INNER ANGLE C =2.8°
Now we can use the LAW OF SINES to find the LENGHT OF SIDE "a"(lower case) (DISTANCE from A to C)(Which is Distance from Satellite to Station A)
DISTANCE FROM A TO C is referred to side "b" (lower case), as it is the side across from the INNER ANGLE B, same as side "c" (lower case) is DISTANCE FROM A TO B, as it is across from INNER ANGLE C, which is 60 Miles.
LAW OF SIGNS EQUATION
b/sinB= c/sinC which means:
b/sin(84.2)=60/sin(2.8)
Which equates to c=90sin84.2/sin(2.8)
Which = 1221.967 (DISTANCE FROM SATELLITE TO A)
NOW to find the DISTANCE FROM THE SATELLITE TO GROUND: Draw a straight line down from satellite making a new RIGHT TRIANGLE.
Even though it is a RIGHT TRIANGLE (Call it XAC, X being the GROUND ANGLE) you can still use the Law of Sines to figure out the HEIGHT FROM GROUND TO SATELLITE.
This is where the 87° ANGLE comes in. With the new RIGHT TRIANGLE we have created, we know 2 of the interior angles: 87° and 90°. to find last interior angle just add together and subtract from 180.
180°-(87°+90°)=3°
Since we know side a SIDE "a" from previous Triangle, it now just becomes SIDE "x" (DISTANCE FROM A TO SATELLITE) which is 1221.967 miles.
Now use LAW OF SINES to find new side A (DISTANCE FROM X(GROUND) to SATELLITE(C)
The equation would be:
a/sinA=x/sinX which is
a/sin87=1221.967/sin90 which equates:
1221.967sin(87)/sin90=
1220.293 miles(DISTANCE FROM SATELLITE TO GROUND)
Very long and hard problem especially without image which I shall add. Good effort to everyone who tried to answer problem, it was correct if ANGLE A was inside the 2 SATELLITES, unfortunately it just wasn't the right way to find the answer that the actual question being asked (or I assume the actual question since I had it in my homework as well, if not i apologize), which again was impossible to know without the image the problem gave.
I could never find the right answer for this problem so I made this to try and help others once I finally found the right answer so I wanted to add this. (And I did finally get correct on the homework so I know this is correct, my problem simply had the distance from A to B as 80 Miles so I just reworked it for this problem with 90 miles instead. It is the same procedure no mater the values you are given, just replace them with the ones you're being asked)
HOPE THIS HELPS =]