Chapter 1 - Section 1.5 - Equations - 1.5 Exercises - Page 56: 41

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

$Solve$ $the$ $equation$ $for$ $the$ $indicated$ $variable:$ $a^2 +b^2 = c^2;$ $for$ $b$ Solve for $b$ Subtract $a^2$ from both sides $a^2+b^2 - a^2 = c^2 - a^2$ $b^2 = c^2-a^2$ Square root both sides $\sqrt {b^2} = \pm \sqrt {c^2-a^2}$ $b = \pm \sqrt {c^2-a^2}$