Law of Sines Calculator
Enter side a, angle A (opposite a), and side b to solve the triangle.
The Law of Sines states that in any triangle, each side divided by the sine of its opposite angle is constant. It is used to solve triangles when you know an angle-side pair plus another angle or side.
- 1The ratio a/sin(A) = b/sin(B) = c/sin(C)
- 2Use when given: AAS, ASA, or SSA (be careful — SSA can give 0, 1, or 2 solutions)
A=30°, B=45°, a=10=b ≈ 14.1410/sin30° = b/sin45° → b=10√2
The ambiguous case (SSA)
Given two sides and a non-included angle, there may be zero, one, or two valid triangles. Always check if the computed sine value is ≤ 1.
| Ratio | Form |
|---|---|
| Basic | a/sin(A) = b/sin(B) = c/sin(C) |
| Find side b | b = a·sin(B)/sin(A) |
| Find angle B | sin(B) = b·sin(A)/a |
References
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