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📘 About the Triangle Calculator
Every triangle is fixed by three of its six measurements, as long as one is a side. The law of cosines handles three sides (SSS) and two sides with the angle between them (SAS); the law of sines handles two angles and a side (ASA, AAS) and the ambiguous case of two sides and an angle not between them (SSA), which can have two different triangles.
Fill in any three boxes. The calculator chooses the method, finds the missing sides and angles (both triangles in the ambiguous case), and gives the area, perimeter, the type (scalene, isosceles, right-angled, obtuse …), the three heights and the inradius and circumradius.
🧮 Formula
✏️ Worked examples
SAS: a = 5, b = 7, C = 60°
You get| Sides | a = 5, b = 7, c = 6.244998 |
| Angles | A = 43.89789°, B = 76.10211°, C = 60° |
| Area · perimeter | 15.155445 · 18.244998 |
| Type | Scalene, acute |
| Heights (to a, b, c) | 6.06218, 4.33013, 4.85363 |
| Inradius · circumradius | 1.66133 · 3.60555 |
| Method | SAS — law of cosines |
a = 5, b = 7, c = 6.244998.
SSA ambiguous case
You get| Triangle 1: Sides | a = 10, b = 15, c = 19.60476 |
| Triangle 1: Angles | A = 30°, B = 48.59038°, C = 101.4096° |
| Triangle 1: Area · perimeter | 73.517848 · 44.604759 |
| Type | Scalene, obtuse |
| Heights (to a, b, c) | 14.7036, 9.80238, 7.5 |
| Inradius · circumradius | 3.29641 · 10 |
| Method | SSA — law of sines (ambiguous case) |
| Triangle 2: Sides | a = 10, b = 15, c = 6.376003 |
| Triangle 2: Angles | A = 30°, B = 131.4096°, C = 18.59038° |
| Triangle 2: Area · perimeter | 23.91001 · 31.376003 |
a = 10, b = 15, c = 19.60476.
🧭 How to use this calculator
What you enter
- Side a
- Side b
- Side c
- Angle A (opposite a) (°)
- Angle B (opposite b) (°)
- Angle C (opposite c) (°)
What you get
- Sides
- Angles
- Area · perimeter
- Type
- Heights (to a, b, c)
- Inradius · circumradius
- Method
❓ Frequently asked questions
When is a triangle ambiguous?
With two sides and an angle opposite one of them (SSA). If the side opposite the angle is shorter than the other side but long enough, two triangles fit.
How do I find an angle from three sides?
Use the law of cosines: cos A = (b² + c² − a²)/(2bc).
Which side is a?
Side a is opposite angle A, b opposite B and c opposite C.
