# Using the Pythagorean Theorem, how do you find the length of a leg of a right triangle if the other leg is 7 feet long and the hypotenuse is 10 feet long?

Jan 26, 2017

See the entire solution process below:

#### Explanation:

The Pythagorean Theorem states:

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

Where $a$ and $b$ are legs of a right triangle and $c$ is the hypotenuse.

Substituting the values for the problem for one of the legs and the hypotenuse and the solving for the other leg gives:

${a}^{2} + {7}^{2} = {10}^{2}$

${a}^{2} + 49 = 100$

${a}^{2} + 49 - \textcolor{red}{49} = 100 - \textcolor{red}{49}$

${a}^{2} = 51$

$\sqrt{{a}^{2}} = \sqrt{51}$

$a = \sqrt{51} = 7.14$ rounded to the nearest hundredth.