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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.

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

$\begin{array}{l}{x}^2+{\left(x\sqrt{3}\right)}^2=x^2+3x^2\\ =4x^2\\ ={\left(2x\right)}^2\end{array}$