Law of Sines Calculator

a/sin(A) = b/sin(B) = c/sin(C). Solve any triangle given AAS / ASA / SSA.

Inputs

Result

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How to use this calculator

  • Enter angle A and its opposite side a.
  • Enter angle B.
  • Read computed angle C and remaining sides.

About this calculator

Law of sines: a/sin(A) = b/sin(B) = c/sin(C) = 2R (where R = circumradius). Use to solve triangles when you know two angles and one side (AAS or ASA): the third angle is 180° − A − B, then ratios give the missing sides. The SSA case ("ambiguous case") can have 0, 1, or 2 valid triangles depending on configuration.

Frequently asked

When does law of sines work?+
Best for AAS, ASA, or SSA triangles (one side + opposite angle, plus one more piece). For SAS or SSS, use law of cosines.
Why does C = 180° − A − B?+
Triangle interior angles sum to 180°. Once you know two, the third follows.
Ambiguous case (SSA)?+
Given two sides + non-included angle, sometimes 0, 1, or 2 solutions exist. This calc takes AAS only.
Why 2R appears?+
The common ratio in law of sines equals the diameter of the circumscribed circle. Useful in extended trigonometry.
Real-world use?+
Surveying (measuring distances using known angles), navigation, and any triangulation problem.

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