Question

1. solve for b: $a^2 + b^2 = c^2$

Explanation:

Step1: Isolate \( b^2 \)

Subtract \( a^2 \) from both sides of the equation \( a^2 + b^2 = c^2 \) to get \( b^2 = c^2 - a^2 \).

Step2: Solve for \( b \)

Take the square root of both sides. Remember that when taking the square root, we consider both positive and negative roots, so \( b = \pm\sqrt{c^2 - a^2} \).

Answer:

\( b = \pm\sqrt{c^2 - a^2} \)