Law of Sines Calculator
Including the ambiguous case, with both answers.
Work out Law of Sines. Including the ambiguous case, with both answers. Shows the working, not just the answer.
The side opposite the known angle.
The side whose opposite angle you want.
Angle B
49.886°
Ambiguous case — 130.114° also works
a/sin A = b/sin B = c/sin C. This is the ambiguous case, and the ambiguity is real geometry rather than a rounding problem: with two sides and a non-included angle, two genuinely different triangles can satisfy the same measurements. Both are shown, and only the context of your problem can decide which is meant. Reporting just the acute one is the standard way this gets marked wrong. The two candidate angles are always supplementary — they add to 180° — because sine takes the same value at an angle and at its supplement.
How the Law of Sines Calculator works
Enter a side, its opposite angle, and a second side to find that side's opposite angle. Where two different triangles satisfy the same measurements — the ambiguous case — both are given, because reporting only the acute one is the standard way this comes out wrong.
Also known as: sine rule calculator · ambiguous case calculator · ssa triangle calculator · two possible triangles calculator
Frequently asked questions
What is the law of sines?
a/sin A = b/sin B = c/sin C. Each side divided by the sine of its opposite angle gives the same value for all three.
What is the ambiguous case?
With two sides and a non-included angle (SSA), two genuinely different triangles can fit the same measurements. Sine gives the same value at an angle and at its supplement, so both an acute and an obtuse answer may be valid.
How do I know which of the two answers is right?
The measurements alone cannot tell you — only the context can. If the obtuse answer would push the angle total past 180° it is impossible and there is only one triangle, which this page checks for you.
Why does it sometimes give no answer at all?
Because the required sine would exceed 1, which no angle produces. Geometrically the second side is too short to reach and close the triangle at that angle.
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