Whats the advanced version and simplified version of the Pythagorean theorem solution

Pythagorean theorem is the equation set up/formula for solving equations for right triangles. I’m sure your familiar with
a squared plus b squared equals c squared. ( a^+b^=c^ )
That’s the simplified version!
The more you start to learn about it like in Geometry and in collage, the more complex it gets. Such as...
Finding the hypotenuse on the triangle
Hypotenuse=c^ in the simplified equation. The hypotenuse is always the longer side of the right triangle. Then from there, since all right triangles have 90 degree angles, after finding the 90 degree angle on the triangle, across from the degree, is the leg that we would label O for opposite. Leaving us with one last leg which we would label adjacent