Enter Triangle Values
Supported patterns: any two angles, all three sides, one included angle with two adjacent sides (SAS), or one angle with its opposite side and one extra side (SSA).
Example Data Table
Sample cases for quick testing| Case | Known Inputs | Calculated Angles | Triangle Type |
|---|---|---|---|
| Angle Sum | A = 35°, B = 65° | C = 80° | Acute Triangle |
| SSS | a = 3, b = 4, c = 5 | A = 36.87°, B = 53.13°, C = 90° | Right Triangle |
| SAS | A = 60°, b = 7, c = 9 | A = 60°, B = 46.10°, C = 73.90° | Acute Triangle |
| SSA Ambiguous | A = 30°, a = 10, b = 12 | B = 36.87° or 143.13° | Two Possible Triangles |
Formula Used
1) Triangle Angle Sum Rule
When any two angles are known, the third angle equals 180° minus their sum.
2) Law of Cosines
cos(B) = (a² + c² − b²) / (2ac)
cos(C) = (a² + b² − c²) / (2ab)
Use this when all three sides are known, or when an included angle and two adjacent sides are known.
3) Law of Sines
Use this when one angle and its opposite side are known together with one other side. This can create one or two valid triangles.
4) Triangle Validity Checks
Three side lengths must satisfy the triangle inequality before angle calculations are valid.
How to Use This Calculator
- Enter any supported set of measurements in the angle and side fields.
- For quick angle completion, enter any two angles.
- For a full side-based solution, enter all three sides.
- For SAS, enter one included angle and the two sides touching that angle.
- For SSA, enter one angle, its opposite side, and one additional side.
- Click Find Triangle Angles to show the result above the form.
- Review the steps, chart, and any ambiguity notes.
- Use the CSV and PDF buttons to download the current results.
FAQs
1) What inputs does this triangle angle finder support?
It supports four common setups: any two angles, all three sides, SAS cases with an included angle, and SSA cases with one angle, its opposite side, and another side.
2) Why can one input set produce two solutions?
This happens in the ambiguous SSA case. The Law of Sines can create two different second angles that both satisfy the same sine value, producing two valid triangles.
3) Why does the calculator reject some side lengths?
Three sides must satisfy the triangle inequality. If one side is longer than or equal to the sum of the other two, the shape cannot close into a triangle.
4) Are angles measured in degrees or radians?
This calculator uses degrees for all angle inputs and outputs. Enter values like 30, 45, or 120 rather than radian-based values.
5) Can I use this for homework and engineering sketches?
Yes. It is useful for geometry homework, drafting checks, surveying approximations, and quick design reviews where triangle angle relationships matter.
6) What does the angle chart show?
The Plotly chart compares the final angle values for each solution. When two triangles are possible, it displays both result sets side by side.
7) Does entering extra values improve accuracy?
Extra values can help with validation, but they are not always required. Some modes only need angles, while others depend entirely on side measurements.
8) What do the CSV and PDF downloads include?
The downloads include the solved angles, angle sum, triangle classification, and any computed side generated during ambiguous SSA cases.