# Using Isosceles Right Triangles

The *isosceles right triangle,* or the 45-45-90 right triangle, is a special right triangle. The two acute angles are equal, making the two legs opposite them equal, too. What’s more, the lengths of those two legs have a special relationship with the hypotenuse (in addition to the one in the Pythagorean theorem, of course).

In an isosceles right triangle, if the legs are each *a* units in length, then the hypotenuse is

or about 1.4 times as long as a leg.

Now that you know how isosceles right triangles work, try your hand at this sample problem: If an isosceles right triangle has a hypotenuse that’s 16 units long, then how long are the legs?

Create an equation to solve.

The hypotenuse is

where

*a*is the length of the legs. You know that the hypotenuse is 16, so you can solve the equationfor the length of

*a*.Solve for

*a*.Divide each side by the radical to get

Each leg is about 11.3 units.