Last updated October 13, 2026 · Report an error
The law of sines relates a triangle's sides to the sines of their opposite angles, letting you solve a triangle completely once you know two angles and one side.
This calculator solves a triangle from two known angles and one side.
How it works
Enter two angles and the side opposite the first angle. The calculator finds the third angle (since all three always sum to 180°), then applies the law of sines ratio to find both remaining sides.
- Enter angle A (degrees).
- Enter angle B (degrees).
- Enter side a (opposite angle A).
- Click Calculate to see your results.
Examples
A = 50°, B = 60°, a = 10
With angle A = 50°, angle B = 60°, and side a = 10, the third angle C works out to 70°, with side b ≈ 11.31 and side c ≈ 12.27.
Who should use it
- Solving a triangle from two angles and one side for a trigonometry course.
- Finding unknown distances in surveying or navigation problems given angle measurements.
Industry applications
- Trigonometry and mathematics education
- Surveying, navigation, and engineering
Advantages
- Solves the triangle completely — all three angles and all three sides.
- Avoids the ambiguous SSA case entirely by design, so results are always unambiguous.
Limitations
- Doesn't handle the SSA case — use the law of cosines or a dedicated ambiguous-case solver for that.
Common mistakes to avoid
- Trying to use this tool for the ambiguous SSA case (two sides and a non-included angle) — that case can have zero, one, or two solutions and isn't handled here.
- Mismatching which side is "opposite" which angle — side a must be opposite angle A specifically.
Best practices
- Use the law of sines when you know two angles (AAS/ASA); use the law of cosines instead when you know two sides plus the included angle, or all three sides.
Tips
- Once you know any triangle's three angles and one side, the law of sines lets you find the other two sides directly — a common technique in triangulation and surveying.
Frequently asked questions
Yes, with no signup and no limit on how many triangles you solve.
When two angles and one side are known (AAS or ASA), there's always exactly one valid triangle — the alternative case (SSA, two sides and a non-included angle) is mathematically ambiguous and can have zero, one, or two valid solutions, so it's deliberately excluded from this tool.
In standard triangle notation, each lowercase side letter is opposite the uppercase angle with the matching letter — side a is the side that doesn't touch vertex A, directly across from it.
All three angles in any triangle always sum to exactly 180° — if the two given angles already summed to 180° or more, there would be no positive angle left for the third one, meaning no valid triangle exists.