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30°-60°-90° Triangles

There is a special relationship among the measures of the sides of a 30°60°90° triangle.

A 30°60°90° triangle is commonly encountered right triangle whose sides are in the proportion 1:3:2. The measures of the sides are x, x3, and 2x.

In a 30°60°90° triangle, the length of the hypotenuse is twice the length of the shorter leg, and the length of the longer leg is 3 times the length of the shorter leg.

To see why this is so, note that by the Converse of the Pythagorean Theorem, these values make the triangle a right triangle.