30-60-90 Triangle Calculator
Solve any triangle from three known values — SSS, SAS, ASA, AAS or SSA — and get every side, every angle, the area, the perimeter and the heights, with the law of sines and cosines steps written out and a scaled diagram.
Result
The 30-60-90 triangle is the special right triangle whose sides always come in the exact ratio 1 : √3 : 2: the shortest side faces the 30° angle, the middle side (√3 ≈ 1.73205 times the short one) faces 60°, and the hypotenuse — exactly twice the short side — faces the right angle.
This page opens the calculator in the ASA case with the defining example prefilled: angles of 30° and 60° joined by a side of length 2, which plays the role of the hypotenuse. Solving it produces the remaining 90° angle and the sides 1 and √3, confirming the ratio, along with the area (√3/2 ≈ 0.866), the perimeter and the heights on a scaled diagram.
The shape is half of an equilateral triangle cut along its height, which is why it appears in hexagons, roof pitches and trigonometry tables: sin 30° = 1/2 and cos 30° = √3/2 are literally read off its sides. Enter your own pair of angles and one known side to solve any similar triangle at a different scale.