1. The problem is to express $b$ in terms of $a$ and $c$ from the Pythagorean theorem equation: $$a^2 + b^2 = c^2$$ 2. To isolate $b^2$, subtract $a^2$ from both sides: $$b^2 = c^2 - a^2$$ 3. To solve for $b$, take the square root of both sides: $$b = \pm \sqrt{c^2 - a^2}$$ 4. The $\pm$ indicates two possible values for $b$, positive or negative, depending on the context. 5. Therefore, the solution for $b$ is: $$b = \pm \sqrt{c^2 - a^2}$$