All Three Sides

Knowing any one side of a 30-60-90 triangle, you can find the other two. Work through the short leg: it is the key to the ratio 1 : √3 : 2.

Here the long leg QR, facing the 60° angle at P, is $6\cdot \sqrt{3}$. The long leg is the short leg times √3, so the short leg is 6. Then the hypotenuse is twice the short leg, 12. From the hypotenuse it works the same way: halve it for the short leg, then multiply by √3.

On the stage you can find the sides in either order. Each one is a step with Special right triangle, or Pythagorean theorem once two sides are known.