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Law of Sines Calculator
Solve any triangle using the Law of Sines: a/sin(A) = b/sin(B) = c/sin(C). Works for ASA, AAS, and SSA triangle configurations.
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The Law of Sines: a/sin(A) = b/sin(B) = c/sin(C). Enter any 3 values (at least one side + one angle, or two angles + one side) to solve the triangle.
Sides
Angles (degrees)
Fonctionnalités Clés — Law of Sines Calculator
Solves ASA, AAS triangle configurations
Finds all sides, angles, and area
Automatic missing angle calculation (A+B+C=180°)
Sine ratio output
Triangle inequality validation
Pourquoi Utiliser Cet Outil — Law of Sines Calculator
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Questions Fréquemment Posées — Law of Sines Calculator
What is the Law of Sines?
The Law of Sines states: a/sin(A) = b/sin(B) = c/sin(C), where a, b, c are sides and A, B, C are the opposite angles. This ratio equals the diameter of the triangle's circumscribed circle. It is used to solve triangles when you know two angles and a side (ASA or AAS) or two sides and a non-included angle (SSA, ambiguous case).
When do I use the Law of Sines vs Law of Cosines?
Use Law of Sines for: ASA (two angles + included side), AAS (two angles + any side), or SSA (two sides + non-included angle). Use Law of Cosines for: SSS (three sides) or SAS (two sides + included angle). The Law of Cosines is more generally applicable and avoids the ambiguous case.
What is the ambiguous case (SSA)?
When given two sides and a non-included angle (SSA), there may be 0, 1, or 2 valid triangles — this is the ambiguous case. If a < b·sin(A), no triangle exists. If a = b·sin(A), exactly one (right) triangle exists. If a ≥ b, exactly one triangle. If b·sin(A) < a < b, two triangles exist. This calculator returns the principal solution.