The law of sines
The law of sines says that in any triangle, each side divided by the sine of its opposite angle gives the same ratio: a / sin A = b / sin B = c / sin C. This calculator uses it to solve a triangle when you know two angles and one side — the AAS or ASA case — returning the third angle, the other two sides, the area, and the perimeter.
How it solves
The two angles give the third immediately, since they sum to 180 degrees. The known side and its opposite angle fix the common ratio, and multiplying that ratio by the sine of each other angle produces the remaining sides.
The ambiguous case
When you instead know two sides and an angle not between them (SSA), the law of sines can yield zero, one, or two valid triangles. That ambiguity is why this tool uses the clean two-angle-and-a-side setup; for side-heavy data, the law of cosines is safer.
Related tools
For two sides and the included angle, or all three sides, use the law of cosines calculator. For 90-degree triangles, the right triangle calculator.
Worked example
With angle A = 40, angle B = 60, and side a = 10: angle C is 80, the ratio is about 15.56, so side b is about 13.47 and side c about 15.32.
FAQ
Which side must I enter?
The side opposite angle A. Pairing a side with its opposite angle is what sets the ratio the law of sines needs.
What if the two angles sum to 180 or more?
Then no triangle exists — the three angles must total exactly 180 — and the calculator flags it.