Law of Sines Calculator (Solve a Triangle from Two Angles and a Side)
Enter side a, its opposite angle A, and angle B.
Your numbers
Your results
Angle C (degrees)
Angle C (degrees)
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Side b
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Side c
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Area
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Perimeter
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Circumradius
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Law of Sines Calculator (Solve a Triangle from Two Angles and a Side) by TheCalcTools
How the Law of Sines Calculator (Solve a Triangle from Two Angles and a Side) works
The law of sines says a/sin A = b/sin B = c/sin C = 2R, where R is the radius of the circle through the three corners. With two angles known, the third is 180° minus their sum.
Given two sides and a non-included angle (SSA), there can be two triangles; this calculator handles the unambiguous AAS and ASA cases.
The formula
a/sin A = b/sin B = c/sin C = 2R
Worked example
Using the default values shown in the calculator:
| Side a | 10 |
|---|---|
| Angle A (opposite a, degrees) | 40 |
| Angle B (degrees) | 75 |
- a = 10, A = 40°, B = 75°: C = 65.0000°.
- b = 15.0271, c = 14.0996, area 68.0961.
Result:
| Angle C (degrees) | 65.0000 |
|---|---|
| Side b | 15.0271 |
| Side c | 14.0996 |
| Area | 68.0961 |
| Perimeter | 39.1268 |
| Circumradius | 7.7786 |
Frequently asked questions
When should I use the law of cosines instead?
When you know three sides, or two sides and the angle between them.
Sources and further reading
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This calculator gives estimates for information only. Check important results independently before you rely on them. See our disclaimer.