Law of Sines Calculator 2025
Solve any triangle (AAS, ASA, SSA) and visualize the results.
Triangle Inputs
Enter any three values (at least one side). The calculator will detect the case (AAS, ASA, SSA) and solve.
Triangle Visualization
Calculation Log
Enter values to see the steps...
Law of Sines FAQ
What is the Law of Sines?
The Law of Sines is a rule used in trigonometry to find unknown angles or sides of an oblique triangle (a triangle with no right angle). It states that the ratio of the length of a side of a triangle to the sine of its opposite angle is the same for all three sides.
a / sin(A) = b / sin(B) = c / sin(C)
When can I use the Law of Sines?
You can use the Law of Sines if you know:
- Angle-Angle-Side (AAS): Two angles and a non-included side.
- Angle-Side-Angle (ASA): Two angles and their included side.
- Side-Side-Angle (SSA): Two sides and a non-included angle. This is the "ambiguous case."
What is the Ambiguous Case (SSA)?
When you are given two sides and a non-included angle (SSA), there might be zero, one, or two possible triangles that can be formed. This calculator automatically detects this case.
- No Solution: If the given side is too short to reach the base of the triangle.
- One Solution: If the given side forms a right triangle or if only one possible angle configuration works.
- Two Solutions: If the given side can swing to form two different valid triangles. This calculator will solve for both possibilities.
