Solve any triangle using the Law of Sines Calculator. Enter three known values — choose a solve mode (find a missing side or angle), then provide the corresponding sides (a, b, c) and angles (A, B, C) in degrees or radians. You'll get the missing side or angle, plus the full triangle's perimeter and area.
Result
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Angle Sum (A + B + C)
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Perimeter
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Area
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Triangle Type
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The Law of Sines states that in any triangle, the ratio of a side length to the sine of its opposite angle is constant: a/sin(A) = b/sin(B) = c/sin(C). This relationship holds for all triangles — not just right triangles — and can be used to find unknown sides or angles when you know at least one opposite angle-side pair.
You can use the Law of Sines when you know two angles and one side (AAS or ASA), or two sides and a non-included angle (SSA). It does not directly apply when you only know three sides (SSS) or two sides and the included angle (SAS) — those cases require the Law of Cosines.
Yes, the Law of Sines applies to right triangles as well as oblique (non-right) triangles. However, right triangles can often be solved more simply using basic trigonometry (SOH-CAH-TOA). The Law of Sines is especially useful for oblique triangles where right-triangle trig does not directly apply.
The ambiguous case occurs when you know two sides and a non-included angle (SSA). In this configuration, there may be zero, one, or two valid triangles. Whether 0, 1, or 2 solutions exist depends on the relative lengths of the known sides and the size of the known angle. Always check which scenario applies before accepting a single answer.
In standard notation, side a is always opposite Angle A, side b is opposite Angle B, and side c is opposite Angle C. Mixing up these pairs is the most common mistake when applying the Law of Sines, and will produce incorrect results. Always confirm your opposite pairs before entering values.
To convert degrees to radians, multiply by π/180. To convert radians to degrees, multiply by 180/π. For example, 60° = 60 × π/180 ≈ 1.0472 radians. This calculator accepts both units — just select the correct option in the Angle Unit field.
The Law of Sines (a/sin A = b/sin B = c/sin C) is used when you have angle-side pairs, while the Law of Cosines (c² = a² + b² − 2ab·cos(C)) is used when you know three sides or two sides and the included angle. Both laws together can solve any triangle given enough information.
Yes — once you know any three independent parts of a triangle (including at least one side), you can generally find all remaining sides and angles using the Law of Sines and the angle-sum property (A + B + C = 180°). Enter three values in this calculator and it will compute the missing measurements for you.