Law of Sines & Cosines Calculator
Solve any triangle using the Law of Sines or Law of Cosines.
Law of Sines (use when you have ASA or SSA)
a/sin(A) = b/sin(B) = c/sin(C)
Law of Cosines (use when you have SAS or SSS)
c² = a² + b² − 2ab·cos(C)
Side c
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Angle A
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Angle B
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Area
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When to Use Each Law
Law of Sines
Use when you know:
- ASA: Two angles and the included side
- SSA: Two sides and a non-included angle (watch for ambiguous case)
Law of Cosines
Use when you know:
- SAS: Two sides and the included angle
- SSS: Three sides
Ambiguous Case (SSA)
When given SSA, there may be 0, 1, or 2 possible triangles. This depends on whether the opposite side is shorter than, equal to, or longer than the altitude from the known angle.
Frequently Asked Questions
What is the ambiguous case?
The ambiguous case occurs with SSA (two sides and a non-included angle). Depending on the values, there might be 0, 1, or 2 valid triangles that satisfy the given conditions.