Law of Sines Calculator
The law of sines states that in any triangle, the ratio of a side to the sine of its opposite angle is constant: a/sin(A) = b/sin(B) = c/sin(C). This calculator solves any triangle given either AAS (angle-angle-side), ASA (angle-side-angle), or SSA (side-side-angle) configurations. For SSA, the ambiguous case may yield 0, 1, or 2 solutions.
Law of sines
a / sin(A) = b / sin(B) = c / sin(C)
b = a * sin(B) / sin(A)
c = a * sin(C) / sin(A)
A + B + C = 180°
When to use
| Case | Given | Method |
|---|---|---|
| AAS | Two angles, one side | Find third angle, use law of sines |
| ASA | Two angles, included side | Find third angle, use law of sines |
| SSA (ambiguous) | Two sides, non-included angle | Use law of sines (may have 2 solutions) |
Law of sines calculator: frequently asked questions
What is the law of sines?
For any triangle: a/sin(A) = b/sin(B) = c/sin(C), where lowercase letters are sides and uppercase letters are opposite angles.
When do I use law of sines?
Use it when you know AAS (angle-angle-side), ASA (angle-side-angle), or SSA (side-side-angle, the ambiguous case).
What is the SSA ambiguous case?
When two sides and a non-included angle are known, there may be 0, 1, or 2 possible triangles. This calculator finds all valid solutions.
What angles must sum to?
The three angles of any triangle sum to 180 degrees.
How is this different from law of cosines?
Law of cosines works when you know SSS or SAS. Law of sines works for AAS, ASA, and SSA cases.
Official sources
- Khan Academy: Law of sines.
- NIST: National Institute of Standards.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.