AI Math SolverA 30-60-90 triangle is a special right triangle with fixed side ratios 1 : √3 : 2. Learn the ratio, why it holds, and how to find every side from just one.
Solve it with the AI Math SolverSplit an equilateral triangle in half and you get a 30-60-90 triangle, which is why its side ratios are fixed. The side opposite 30° is the shortest; the hypotenuse is exactly twice it.
Label the short leg x. Then the long leg is x√3 and the hypotenuse is 2x. Given any one side, set it equal to the matching part of the ratio and read off the other two.
It is a right triangle whose angles measure 30°, 60°, and 90°. Its sides always follow the ratio 1 : √3 : 2 — the short leg, long leg, and hypotenuse respectively.
The short leg (opposite 30°) is x. The long leg (opposite 60°) is x√3. The hypotenuse (opposite 90°) is 2x. Knowing one side fixes all three.