# The hypotenuse of a right triangle is 103.1 and one leg is 40. What is the other leg?

Mar 23, 2017

$b = 95.02$

#### Explanation:

The Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. The equation that represents this relationship is:

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

where $c$ is the hypotenuse and $a$ and $b$ are the other two sides.

We know $c$ and one of the other legs, which I'll designate as $a$. So we need to find side $b$.

Rearrange the equation to isolate ${b}^{2}$, substitute the given values into the equation and solve.

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

${b}^{2} = {\left(103.1\right)}^{2} - {40}^{2}$

${b}^{2} = 9029.61$

Take the square root of both sides.

$b = \sqrt{9029.61} = 95.02$