An air traffic controller observes 2 aircraft on a radar screen. The 1st: altitude is 800 m, horizontal distance is 19.2 km and 25 degrees south of west. The 2nd: altitude is 1100 m, horizontal distance is 17.6 km, and 20 degrees south of west. What's the distance between the two aircraft? How would I graph the x axis west, the y axis south, and z vertical?

I suggest taking only two dimensions by two. Consider first the horizontal distances, and assume both planes are at the same altitude for now. You find the distance between them. Your sketch here will be a view from above the planes.

Then, you take into considerations the altitude. You now forget the angles. You will then come up with a right angled triangle, with the base as the distance you found above, and the vertical side as the difference in altitude. You can solve for the distance through Pythagoras' theorem.