# If the hypotenuse is 41 inches and one of the legs is 40 inches, what is the length of the other leg in inches?

Nov 20, 2016

The length of the other leg is $9$ inches

#### Explanation:

As this is a right angle (use of word hypotenuse means opposite angle is right angle), you can use the Pythagorean theorem. This states that
${x}^{2} + {y}^{2} = {r}^{2}$, or leg 1 squared plus leg 2 squared equals the hypotenuse squared.

So, all you need to do is plug in your known numbers and solve for the unknown variable.

${40}^{2} + {y}^{2} = {41}^{2}$
$1600 + {y}^{2} = 1681$
${y}^{2} = 81$
$y = \sqrt{81}$
$y = 9$
So, the length of the missing leg is 9 inches.

(y cannot be negative 9 because you cannot have a triangle with a negative side!)