Law of Sines Calculator
Solve triangles from angles and a side.
Enter your values
ⓘ Live results
Results
- Side b
- 14.09965
- Side c
- 15.02714
- Angle C
- 75°
- Area
- 68.09606
- Circumradius
- 7.77862
Quick answer
The law of sines states that each side divided by the sine of its opposite angle is the same constant.
a/sin A = b/sin B = c/sin C
How to use the Law of Sines Calculator
- 1Enter two known angles in degrees.
- 2Enter the side opposite the first angle.
- 3Read the remaining sides and angle.
Worked example
Using the values the calculator loads with:
Inputs
- Angle A40 degrees
- Angle B65 degrees
- Side a (opposite A)10
Results
- Side b14.09965
- Side c15.02714
- Angle C75°
- Area68.09606
- Circumradius7.77862
Frequently asked questions
What is the ambiguous case?
With two sides and a non-included angle, there may be two valid triangles.
What is the circumradius?
Half the common ratio a/sin A — the radius of the circle through all three vertices.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.