Alright, I think I got it. First, this theorem only works for right triangles. Now, even though there's three variables, you can solve it with only one known. That would be the angle between sides X and Z or Y and Z, so lets call the angle between X and Z, 'theta'. Now, if you solve the equation for X you get X= Sqrt ((X sec theta)^2)-((X tan theta)^2). Now if you want to pull the X's out of there to solve in terms of Theta, well then you've got me.
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Since we were being extreme for so long I got really hungry so we went to Mcdonalds and got some chicken mcnuggets. -Skimack