Hello, Shmomo89!
repcvt gave you an excellent game plan . . .
Plane $\displaystyle A$ flies a distance of 220 miles in the direction N20°E.
Plane $\displaystyle B$ flies a distance of 365 miles from the same airport in the direction S55°W.
Calculate the distance between the two planes. Code:

 o A
 **
 * *
 * *
 * *
 * *
* * 220
*  *
* 20°*
*  *
*  *
* *
       *      o        
* *55°O
* * 
* * 365 
* * 
B o 
We find that $\displaystyle \angle AOB = 145^o$
Now use the Law of Cosines on $\displaystyle \Delta AOB.$
. . .$\displaystyle AB^2 \;=\;365^2 + 220^2  2(365)(220)\cos145^o$ . . . etc.