Calculator Form
Choose one solving mode. Enter the required values. Results appear above this form after submission.
Example Data Table
| Mode | Example Inputs | Summary |
|---|---|---|
| SSS | a = 7, b = 8, c = 9 | Find all three angles from the three sides. |
| SAS | b = 10, c = 12, A = 35° | Find side a and the remaining angles. |
| AAS / ASA | A = 40°, B = 65°, a = 13 | Find C, then compute sides b and c. |
| RHS | a = 6, b = 8 | Find hypotenuse, area, and acute angles. |
| SSA | a = 8, b = 10, A = 35° | Check whether one or two triangles fit. |
Formula Used
Law of Cosines
a² = b² + c² − 2bc cos(A)
b² = a² + c² − 2ac cos(B)
c² = a² + b² − 2ab cos(C)
Law of Sines
a / sin(A) = b / sin(B) = c / sin(C)
Right Triangle Relations
c² = a² + b²
sin(A) = a / c
cos(A) = b / c
tan(A) = a / b
Area Formulas
Area = ½bc sin(A)
Area = √(s(s−a)(s−b)(s−c))
s = (a + b + c) / 2
Ambiguous SSA Rule
sin(B) = b sin(A) / a
This can return zero, one, or two valid triangles.
How to Use This Calculator
- Select the solving mode that matches your known values.
- Enter the required sides and angles carefully.
- Submit the form to solve the triangle.
- Review the result panel above the form.
- Use the Plotly graphs to inspect the solved shape.
- Download CSV for spreadsheets or PDF for reports.
- Try the example table values to test each mode.
- For right triangles, treat side c as the hypotenuse.
FAQs
1) What does this calculator solve?
It solves missing triangle sides, angles, perimeter, area, and classification. It supports SSS, SAS, AAS or ASA, right triangles, and the SSA ambiguous case.
2) When should I use SSS mode?
Use SSS when all three sides are known. The calculator checks triangle validity first, then uses cosine relationships to find each angle.
3) Why can SSA return two answers?
SSA can be ambiguous because the same side and angle setup may fit two different triangles. The calculator checks both possible angle values and returns every valid solution.
4) What does RHS mean here?
RHS means right triangle solving. This calculator assumes angle C equals 90 degrees, side c is the hypotenuse, and sides a and b are the legs.
5) Which formulas are used internally?
It uses the Law of Cosines, Law of Sines, Pythagorean theorem, standard trigonometric ratios, and Heron’s formula for area.
6) Can I export my result?
Yes. After a successful calculation, you can download a CSV summary or generate a PDF report with the solved values and notes.
7) Why do I see an input error sometimes?
Errors appear when values cannot form a real triangle. Common issues include invalid angle totals, impossible side lengths, or a hypotenuse that is too short.
8) Is this tool useful for learning geometry?
Yes. Each result includes steps, formulas, a graph, and triangle classification. That makes it useful for homework checks, revision, and classroom demonstrations.