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# Special right triangles review

Learn shortcut ratios for the side lengths of two common right triangles: 45°-45°-90° and 30°-60°-90° triangles. The ratios come straight from the Pythagorean theorem.

## 30-60-90 triangles

30-60-90 triangles are right triangles whose acute angles are 30, degrees and 60, degrees. The sides in such triangles have special proportions:
A thirty-sixty-ninety triangle. The length of the shorter leg of the triangle is one half h units. The length of the longer leg of the triangle is square root three over two times h. The length of the hypotenuse of the triangle is h units.

## 45-45-90 triangles

45-45-90 triangles are right triangles whose acute angles are both 45, degrees. This makes them isosceles triangles, and their sides have special proportions:
A forty-five-forty-five-ninety triangle. The length of both legs are k units. The length of the hypotenuse of the triangle is square root of two times k units.
The special properties of both of these special right triangles are a result of the Pythagorean theorem.