Solving a triangle
A triangle has six measurements: three sides and three angles. If you know any three of them, including at least one side, the rest can be found. This is called solving the triangle, and which method applies depends on what you know: SSS (three sides), SAS (two sides and the angle between them), ASA or AAS (two angles and a side) or SSA (two sides and an angle opposite one of them).
This calculator finds the missing sides and angles, the area, the perimeter, the three heights, and the radii of the inscribed and circumscribed circles. In the SSA case there can be two valid triangles, and it shows both.
How it is calculated
Law of cosines: c² = a² + b² − 2ab cos C
Law of sines: a ÷ sin A = b ÷ sin B = c ÷ sin C
Heron's formula: area = √(s(s − a)(s − b)(s − c)), s = half the perimeter
Angles add up to 180°
Worked example
Sides 5, 6 and 7
- Angles A · B · C
- 44.42° · 57.12° · 78.46°
- Perimeter
- 18
- Area
- 14.7
- Type
- scalene, acute
Classifying triangles
| By sides | Meaning |
|---|---|
| Equilateral | All three sides equal |
| Isosceles | Two sides equal |
| Scalene | No sides equal |
| Acute / Right / Obtuse | Largest angle below, equal to or above 90° |
Three angles alone cannot fix the size of a triangle, so at least one side length is always needed.