Law of Sines Calculator
Solve a triangle using a/sin A = b/sin B = c/sin C.
Inputs
Use cases ASA, AAS, or SSA
Solution
Enter values and click solve.
The Law of Sines
For any triangle, the ratio of a side to the sine of the opposite angle is constant: a/sin A = b/sin B = c/sin C. This works for ASA, AAS, and (with care) SSA cases. SSA may have zero, one, or two valid solutions — the "ambiguous case".
Frequently Asked Questions
What is the Law of Sines?▾
For any triangle, the ratio of each side to the sine of its opposite angle is constant: a/sin A = b/sin B = c/sin C.
When can I use the Law of Sines?▾
When you know a side and its opposite angle, plus one more piece of information. This covers ASA, AAS, and SSA cases.
What is the SSA "ambiguous case"?▾
In SSA, the given data may produce zero, one, or two valid triangles. Always check whether your computed angle's supplement also yields a consistent triangle.
How does the Law of Sines compare to the Law of Cosines?▾
Use Law of Sines when you have a side-angle pair. Use Law of Cosines for SSS or SAS, where no side-angle pair is directly given.