The hypotenuse of a right triangle is 15 inches, and one of its legs is 11 inches. What is the length of the other leg?

1 Answer
Nov 6, 2015

The missing leg, #b#, is #b = sqrt(104)#.

Explanation:

The Pythagorean Theorem is #a^2 = b^2 = c^2#. The #a# and #b# are each leg and the #c# is the hypotenuse. We can plug in our given information and solve like an equation to
find the missing variable.

Since we know #c#, the hypotenuse, is 15, we can put that in our equation. We also know that #a#, one of our legs, is 11, so we can put that into our equation as well. #11^2 + b^2 = 15^2#. This simplifies to #121 + b^2 = 225#. Simplified one more step, we get #b^2 = 104#.

To reverse the exponent, we must do the square root of each side. #sqrt(b^2) = sqrt(104)#. Since #sqrt(104)# is not rational, we will leave it in this form.

The missing leg, #b#, is #b = sqrt(104)#.