Law of Sines Calculator
If one side and its opposite angle are known, the sine rule a/sin A = b/sin B gives every missing side or angle. Both parts are below.
A. Missing Side b — when a, A and B are known
B. Missing Angle B — when a, A and b are known
How to use
- Pick Part A to find a missing side, or Part B to find a missing angle.
- In Part A, enter one side, its opposite angle, and a second known angle — all angles in degrees.
- In Part B, enter two sides and one opposite angle to solve for the unknown angle.
- Check both answers when shown: the ambiguous case can give an acute and an obtuse solution.
Note: Sine rule: a/sin A = b/sin B = c/sin C. A solved angle can have two possible answers (acute and obtuse) — the tool shows both when both are possible.
Tips
- The sine rule needs a side-angle pair: one side and the angle opposite it must both be known.
- In Part B, always look for the second possible angle — the tool checks the ambiguous case for you.
- If your angles add up to more than 180°, the inputs are impossible; recheck the known values.
Frequently Asked Questions (FAQ)
How does the law of sines calculator work?
Give one side with its opposite angle, then add one more known side or angle; the sine rule a/sin A = b/sin B gives the missing values.
What is the sine rule?
For any triangle, a/sin A = b/sin B = c/sin C, so knowing one pair unlocks the rest.
Are angles in degrees?
Yes. Enter angles in degrees, as labelled on the inputs.
Is this calculator free?
Yes, it is completely free to use, with no signup or account needed.