Solve any triangle instantly with the Law of Sines
Select Known Information
You know angles A and B, and side a (opposite to angle A).
a / sin(A) = b / sin(B) = c / sin(C)
Side a is opposite angle A, side b opposite B, side c opposite C
Enter Known Values
Angle C = 180° − 40° − 60° = 80°
Angle A
40°
Angle B
60°
Angle C
80°
Side a
10
Side b
13.472964
Side c
15.320889
Area
66.341395
Perimeter
38.793852
When to Use the Law of Sines
Use the Law of Cosines instead for SAS (two sides + included angle) or SSS (all three sides).
The Law of Sines calculator solves any triangle when you know two angles and a side (AAS or ASA) or two sides and a non-included angle (SSA). Enter your known values and instantly get all missing sides, angles, area, and perimeter. The tool automatically detects the ambiguous SSA case and shows both valid triangle solutions when they exist.
The Law of Sines states that for any triangle, the ratio of a side to the sine of its opposite angle is constant: a/sin(A) = b/sin(B) = c/sin(C). This lets you find unknown sides or angles whenever you know two angles and one side, or two sides and a non-included angle.
The SSA case (two sides and a non-included angle) can produce zero, one, or two valid triangles. When the given side opposite the known angle is shorter than the other known side, two different triangles may satisfy all the given conditions. This calculator detects this and shows both solutions.
Use the Law of Cosines when you know all three sides (SSS) or two sides with the included angle (SAS). The Law of Sines requires at least one known angle, so for SSS or SAS configurations the Law of Cosines is the correct approach.
All angle inputs and outputs use degrees, which is the most common convention in trigonometry courses and real-world applications. The calculator converts internally to radians for computation and always displays results in degrees.