1. The problem states the Pythagorean theorem: $x^2 + y^2 = z^2$. 2. This formula relates the lengths of the sides of a right triangle, where $x$ and $y$ are the legs and $z$ is the hypotenuse. 3. To find one side when the other two are known, rearrange the formula. For example, to find $z$, use: $$z = \sqrt{x^2 + y^2}$$ 4. To find $x$, rearrange as: $$x = \sqrt{z^2 - y^2}$$ 5. Similarly, to find $y$, rearrange as: $$y = \sqrt{z^2 - x^2}$$ 6. Remember, the hypotenuse $z$ is always the longest side, so $z > x$ and $z > y$. 7. This theorem only applies to right triangles, where the angle between sides $x$ and $y$ is 90 degrees. This formula is fundamental in geometry and helps calculate distances in many contexts.