What this calculator does
The law of sines is useful when you know a matching angle-side pair and another angle or side.
When to use the Law of Sines
The law of sines works best when you know an angle and the side opposite that angle. It is commonly used for ASA, AAS, and some SSA problems.
| Case | Known information | Use with care? |
|---|---|---|
| ASA | Two angles and the included side | No, usually straightforward |
| AAS | Two angles and a non-included side | No, usually straightforward |
| SSA | Two sides and a non-included angle | Yes, ambiguous case possible |
Formula reference
The law of sines states:
a / sin(A) = b / sin(B) = c / sin(C)
Side a is opposite angle A, side b is opposite angle B, and side c is opposite angle C. The side-angle pairing is the most important labeling rule.
Step-by-step AAS example
If angle A, angle B, and side a are known, first calculate angle C = 180° − A − B. Then use b = a × sin(B) / sin(A) and c = a × sin(C) / sin(A).
SSA ambiguous case
In SSA, the same known side, second side, and angle may create two possible triangles. This is why the calculator may report multiple solutions. If your assignment expects only one, check whether a diagram or additional constraint was provided.
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