Triangle Calculator (Solve Any Triangle: SSS, SAS, ASA)
Choose what you know and enter the values.
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Triangle Calculator (Solve Any Triangle: SSS, SAS, ASA) by TheCalcTools
How the Triangle Calculator (Solve Any Triangle: SSS, SAS, ASA) works
With three sides the law of cosines gives each angle: cos A = (b² + c² − a²) ÷ (2bc). With two sides and the angle between them it gives the third side first. With two angles and the side between them, the law of sines gives the other sides.
Area comes from Heron’s formula; the inradius is area ÷ semi-perimeter and the circumradius abc ÷ (4 × area).
The formula
Worked example
Using the default values shown in the calculator:
| I know | Three sides (SSS) |
|---|---|
| Side a | 7 |
| Side b | 9 |
| Side c | 12 |
| Angle C between sides a and b (degrees) | 60 |
| Angle A (degrees) | 40 |
| Angle B (degrees) | 60 |
- Sides 7, 9 and 12 give angles 35.430945, 48.189685, 96.37937.
- Area 31.3050; the triangle is Scalene, obtuse.
Result:
| Sides a, b, c | 7, 9, 12 |
|---|---|
| Angles A, B, C (degrees) | 35.430945, 48.189685, 96.37937 |
| Area | 31.3050 |
| Perimeter | 28.0000 |
| Height to side c | 5.2175 |
| Inradius | 2.2361 |
| Circumradius | 6.0374 |
| Type | Scalene, obtuse |
Frequently asked questions
What about two sides and an angle not between them (SSA)?
That case can have two triangles or none. Use the law of sines calculator and check both solutions.
Sources and further reading
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This calculator gives estimates for information only. Check important results independently before you rely on them. See our disclaimer.