Ambiguous Triangle (SSA) Calculator
Ambiguous Triangle (SSA): calculate results from explicit inputs, with a formula and worked example.
Formula
- Use the units shown beside each field.
- Results update automatically whenever you change an input.
- Displayed values use up to four decimal places, or scientific notation for very small or large numbers. Calculations use standard floating-point arithmetic; exact integer and fraction tools identify their own precision rules.
- Euclidean geometry. Use one consistent length unit; areas and volumes use its square and cube. Degenerate shapes are rejected. Very thin shapes may lose floating-point precision. Reports all valid nondegenerate SSA solutions, including none. Near-tangent cases within 10⁻¹⁴ in sin B are treated as one solution.
Example Calculation
- Angle A (opposite a): 30 °
- Side a: 5 units
- Side b: 8 units
A = 30°, a = 5 and b = 8 yield two valid triangles, with B ≈ 53.1301° or 126.8699°.
Method references
Frequently asked questions
How do I use this calculator?
Enter angle a (opposite a), side a, side b. The result updates automatically. Use Reset to restore the example values.
What method does it use?
sin B = b sin A / a; test B and 180°−B with A+B<180°. Euclidean geometry. Use one consistent length unit; areas and volumes use its square and cube. Degenerate shapes are rejected. Very thin shapes may lose floating-point precision. Reports all valid nondegenerate SSA solutions, including none. Near-tangent cases within 10⁻¹⁴ in sin B are treated as one solution.
Why might a rounded result differ?
The calculation keeps full numeric precision internally, then rounds the displayed result. Rounding intermediate steps by hand can produce a slightly different answer.
Are my inputs saved online?
No. This calculator processes your inputs in your browser. A recently used list stores only calculator names on this device, not your entered values.
Check the assumptions and units before using this result. Read about calculation methods.