30-60-90 triangle

A 30-60-90 triangle is a right triangle with a 30 degree angle, a 60 degree angle,a 90 degree angle. It is special because it side lengths are always in the same ratio. The length of the hypotenuse is twice the length of the shorter leg and the length of the longer leg is $\sqrt{3}$ the length of the shorter leg.

Simply put, the ratio in order of the sides opposite to the angles for any value of $x$ is $x$ : $x$ $\sqrt{3}$ : $2x$

Proof (using trig)

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30-60-90 triangle

Proof (using trig)