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Using Isosceles Right Triangles

The isosceles right triangle, or the 45-45-90 right triangle, has some special properties. For example, the two acute angles are equal, making the lengths of 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).


The following figure shows a sample isosceles right triangle.

An isosceles right triangle.
An isosceles right triangle.

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?

  1. Create an equation to solve.

  2. Solve for a.

    Divide each side by the radical to get


    Each leg is about 11.3 units.

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