Math
Law of cosines
Determine the third side of a triangle from two known sides and the angle between them, then calculate the enclosed area.
Calculators / Math / Law of sines
Law of sines calculator
Use one side and its opposite angle with a second angle to determine the remaining triangle sides without the ambiguous side-side-angle case.
On this page
Side opposite angle B17.32units
Third angle90degrees
Third side20units
Calculator controls
How to calculate
Use one side and its opposite angle with a second angle to determine the remaining triangle sides without the ambiguous side-side-angle case.
Side opposite angle B = a*sin(B*pi/180)/sin(A*pi/180) units; Third angle = 180-A-B degrees; Third side = a*sin((180-A-B)*pi/180)/sin(A*pi/180) units
Worked example
Side opposite angle A: 10; Angle A (degrees): 30; Angle B (degrees): 60.
Side opposite angle B: 17.32 units; Third angle: 90 degrees; Third side: 20 units.
Assumptions and limits
Use one side and its opposite angle with a second angle to determine the remaining triangle sides without the ambiguous side-side-angle case. Use the same length unit throughout. Angles marked degrees use degrees. Results describe ideal geometric shapes.
Results are rounded for display; calculations use unrounded values. Read our calculation methodology.
Understanding the result
Use one side and its opposite angle with a second angle to determine the remaining triangle sides without the ambiguous side-side-angle case.
When this tool is useful
Side opposite angle B = a*sin(B*pi/180)/sin(A*pi/180) units; Third angle = 180-A-B degrees; Third side = a*sin((180-A-B)*pi/180)/sin(A*pi/180) units
Understanding your inputs
| Input | What to enter |
|---|---|
| Side opposite angle A | Enter a number of at least 1e-12 and no more than 1000000000000. |
| Angle A (degrees) | Enter a number of at least 0.000001 and no more than 179.999999. |
| Angle B (degrees) | Enter a number of at least 0.000001 and no more than 179.999999. |
Frequently asked questions
What assumptions does this calculation use?
Use one side and its opposite angle with a second angle to determine the remaining triangle sides without the ambiguous side-side-angle case. Use the same length unit throughout. Angles marked degrees use degrees. Results describe ideal geometric shapes.
How is the result calculated?
Side opposite angle B = a*sin(B*pi/180)/sin(A*pi/180) units; Third angle = 180-A-B degrees; Third side = a*sin((180-A-B)*pi/180)/sin(A*pi/180) units