How do you use the pythagorean theorem to solve for the missing side given a = 7, c = 21?

Aug 23, 2016

$b = 14 \sqrt{2}$

Explanation:

There are 2 possible answers, depending on whether $c$ represents the hypotenuse or one of the shorter sides.

From ${a}^{2} + {b}^{2} = {c}^{2}$, one assume that $c$ is the hypotenuse, but it should be stated.

From ${a}^{2} + {b}^{2} = {c}^{2}$ we can also get ${b}^{2} = {c}^{2} - {a}^{2}$ if we are looking for one of the two shorter sides.

${b}^{2} = {21}^{2} - {7}^{2}$

${b}^{2} = 392$

$b = \sqrt{392} = \sqrt{2 \times 4 \times 49}$

$b = 14 \sqrt{2}$