# The Pythagorean theorem t is used to find missing side lengths in a right triangle. How do you solve for b, in terms of c and a?

Oct 19, 2016

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

#### Explanation:

Given a right triangle with legs of length $a$ and $b$ and hypotenuse of length $c$, the Pythagorean theorem states that

${a}^{2} + {b}^{2} = {c}^{2}$

Solving for $b$:

${b}^{2} = {c}^{2} - {a}^{2}$

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

However, we know that as a length, $b > 0$, so we can throw out the negative result. This leaves us with our answer:

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