# How do you use the Pythagorean Theorem to find the missing side of the right triangle with the given measures: A= 15, B= 20?

Feb 28, 2016

$c = 25$

#### Explanation:

If we know that ${a}^{2} + {b}^{2} = {c}^{2}$, and we are given that $a = 15$ and that $b = 20$, then we can solve for $c$.

Let's do that: ${15}^{2} + {20}^{2} = {c}^{2}$, which we can rewrite as $225 + 400 = {c}^{2}$. This can be simplified to $625 = {c}^{2}$, and to solve for $c$, we just need to get rid of the square. To do that, we just square root both sides, like this: $\sqrt{625} = \sqrt{{c}^{2}}$. This gives us $25 = c$. Nice job!

Feb 28, 2016

$C = 25$ (see other answers for this)
or
$C = 5 \sqrt{7}$

#### Explanation:

Since we were not told that the missing side is the hypotenuse an alternate possibility exists from those given previously.

$C = \sqrt{{20}^{2} - {15}^{2}} = \sqrt{175} = 5 \sqrt{7}$