In a 30-60-90 triangle the sides are x, x√3, and 2x. The side across from 30° is x. Across from 60° is x√3. Across from 90° is 2x. Special right triangles as a set are in Pythagorean theorem and special right triangles.
Find x first
If the short leg is 5, the long leg is 5√3 and the hypotenuse is 10. If you are given the hypotenuse, divide by 2 to get x. If you are given the long leg, divide by √3. Do not mix this list with the isosceles right-triangle list.
45-45-90 is the other frozen ratio, in 45-45-90 triangles. Sine and cosine on these angles are in SOH-CAH-TOA. Formulas as a set are in ACT Math formulas.
The bottom line
Opposite 30° is half the hypotenuse. Opposite 60° is that half times √3.
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