The law of sines relates sides and angles in any triangle, not just right triangles.
About this calculator
The law of sines relates sides and angles in any triangle, not just right triangles. Side a sits opposite angle A, side b opposite B, and so on. The ratio a/sin A stays constant for all three pairs.
Enter two angles and one side to solve the rest (AAS or ASA). Enter all three sides with angles at 0 to recover every angle from the side lengths. The calculator checks the triangle inequality before returning area and perimeter.
Surveyors, navigators, and physics students use this rule when only angle measurements and one baseline are available. For SAS cases (two sides plus the included angle), use the [[law-of-cosines]] calculator instead. For 90° triangles, the [[right-triangle]] calculator is faster. Link to [[triangle]] and [[area]] for general triangle checks.
Common uses
- Solve AAS triangles in trigonometry homework
- Find missing sides when two angles and one baseline are known
- Recover all angles from three measured sides (SSS)
- Navigation problems with bearing angles and one distance
- Verify survey triangle closures before plotting
Frequently asked questions
How do I solve a triangle with angles 40° and 60° and side a = 10?
Angle C = 180° − 40° − 60° = 80°. Then b = 10·sin(60°)/sin(40°) ≈ 13.52 and c = 10·sin(80°)/sin(40°) ≈ 15.32. Leave side b and c as 0 and angle C as 0 before calculating.
When should I use the law of sines vs cosines?
Use sines when you know two angles and a side, or two sides and a non-included angle (with care for the ambiguous SSA case). Use cosines when you have two sides and the included angle, or all three sides.
Can I enter all three sides only?
Yes. Set all three side lengths and leave every angle at 0. The engine derives angles from the side lengths and still reports the common sin ratio.
Why does the calculator reject my angles?
Two known angles must leave room for a third positive angle that sums to 180°. Each angle must stay between 0° and 180° exclusive.