# How do you use the Pythagorean theorem to find the hypotenuse if one leg is 34 and the other leg is 18?

Apr 25, 2017

$c = 38.47$ to two decimal points.

#### Explanation:

The Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. Algebraically, it is color(blue)(c^2=a^2+b^2, where $c$ is the hypotenuse and $a \mathmr{and} b$ are the other two sides.

Known
$a = 18$
$b = 34$

Unknown: $c$

Solution
Plug the known values for $a \mathmr{and} b$ into the equation.

${c}^{2} = {18}^{2} + {34}^{2}$

Simplify.

${c}^{2} = 324 + 1156$

Simplify.

${c}^{2} = 1480$

Take the square root of both sides.

$\sqrt{{c}^{2}} = \sqrt{1480}$

$c = 38.47$ to two decimal points