# Using the Pythagorean Theorem, how do you find the length of side c given a = 20 , b = 28?

Jan 17, 2017

See the entire solution process below:

#### Explanation:

The Pythagorean Theorem states, given a right triangle:
${a}^{2} + {b}^{2} = {c}^{2}$

Where $a$ and $b$ are the base and height of the triangle and $c$ is the hypotenuse.

To solve this problem we substitute the values from the problem for $a$ and $b$ and solve for $c$

${20}^{2} + {28}^{2} = {c}^{2}$

$400 + 784 = {c}^{2}$

$1184 = {c}^{2}$

$\sqrt{1184} = \sqrt{{c}^{2}}$

$\sqrt{1184} = \sqrt{{c}^{2}}$

$34.4 = c$

$c = 34.4$ rounded to the nearest tenth.