Calculator Input
Enter any valid oblique-triangle set. Supported patterns include SSS, SAS, ASA, AAS, and SSA.
Example data table
| Case | Sample inputs | Example output summary |
|---|---|---|
| SSS | a = 7, b = 8, c = 9 | A = 48.1897°, B = 58.4119°, C = 73.3985°, Area = 26.8328 |
| SAS | a = 10, b = 13, C = 47° | c = 9.5750, A = 49.8018°, B = 83.1982° |
| ASA | A = 50°, B = 60°, a = 9 | C = 70°, b = 10.1746, c = 11.0401 |
| SSA | A = 35°, a = 8, b = 11 | Two valid triangles may exist in the ambiguous case. |
Formula used
Law of Sines: a / sin(A) = b / sin(B) = c / sin(C)
Law of Cosines: a² = b² + c² − 2bc cos(A), with matching cyclic forms for b² and c².
Angle sum: A + B + C = 180°
Heron’s Formula: Area = √(s(s − a)(s − b)(s − c)), where s = (a + b + c) / 2
Area with two sides and included angle: Area = 1/2 × ab × sin(C)
Altitudes: ha = 2 × Area / a, and similarly for hb and hc.
How to use this calculator
- Enter any valid set of known triangle values.
- Use at least three independent measures, including one side.
- Enter sides as positive lengths and angles in degrees.
- Choose your preferred decimal precision and unit label.
- Press Solve Triangle to generate the full solution.
- Review the method, checks, graph, and derived measures.
- Download the solution as CSV or PDF when needed.
Frequently asked questions
1. What makes a triangle oblique?
An oblique triangle has no 90-degree angle. Every angle is either acute, or one angle is obtuse. This solver handles both forms.
2. Which input combinations are valid here?
You can solve SSS, SAS, ASA, AAS, and SSA cases. SSA may produce one triangle, two triangles, or no valid triangle.
3. Why does the SSA case sometimes show two answers?
The Law of Sines can produce an acute or supplementary angle. When both satisfy the angle sum and side rules, two distinct triangles exist.
4. Why do I need at least one side?
Angles alone only define shape, not scale. At least one side fixes the size, letting the solver compute perimeter, area, altitudes, and medians.
5. How is the graph drawn?
The graph places one side on the horizontal axis, then computes the third vertex from the solved side lengths. Plotly renders the triangle outline.
6. What causes an invalid result?
Invalid entries include negative values, angles summing above 180 degrees, impossible side combinations, or inconsistent mixed inputs that cannot describe one triangle.
7. Does the calculator round internal values?
No. Internal calculations use full floating-point values. The chosen precision only affects displayed output and exported report formatting.
8. Can I use centimeters, meters, or feet?
Yes. Enter any side unit consistently, then place that label in the unit field. Area will appear automatically in square units.