You mean engineers have sweat all this time to bring you people extremely low-cost calculators (well, at least when assembled in sweat shops), and you don’t know how to use them? This problem is a total no-brainer if you have a scientific calculator (hardware or software) – one that has arctangents on it.
If you know the lengths of the 3 sides of a right triangle and want to know the 2 angles besides the definition-determined 90-deg angle, all you have to do is take the ratio of the 2 shortest sides (i.e., divide them), either way around, and then take the arc- or inverse tangent of the result. Subtract this angle from 90 deg. The 90-deg angle is, of course, opposite the longest side of the triangle, the smallest of the angles found before and after the above subtraction is opposite the smallest angle, and the remaining angle is, then, obviously opposite the remaining side. Of course, trig tables will also get you there in the same manner. You don’t need any fancy formulae (unless you just like to calculate out numerous terms of a long series for an arctangent.
Ray (with plenty of angles for getting off on a tangent)