When to use this calculator
Use the sine rule when one side and its opposite angle are known along with another angle.
Explore the trigonometry calculators for other questions in this topic. For a related calculation, use the Secant Calculator: Find the reciprocal cosine of an angle entered in degrees.
PUTTING IT INTO PRACTICE
Law of Sines Side: a worked example
The values below are an illustrative example, not a recommendation. Replace them with measurements or assumptions that match your question.
| Input | Example value |
|---|---|
| Known side | 10 |
| Angle opposite known side (degrees) | 30 |
| Angle opposite required side (degrees) | 90 |
| Result | 20 units |
- Check the input labels and enter the example values above.
- Apply the relationship: Required side = known side × sin(required angle)/sin(known angle).
- The result is 20 units, rounded for display.
How to interpret your result
The two angles must add to less than 180° so a third positive angle exists.
These tools take degrees unless stated otherwise. A right-triangle ratio and the law of cosines solve different input patterns. For the sine rule, identify which side is opposite each supplied angle.
Frequently asked questions
Are the angle inputs in degrees or radians?
The trigonometry tools here label angles in degrees and convert internally. Use the degree-to-radian converter when another formula requires radians.
When is the law of sines side calculator useful?
Use the sine rule when one side and its opposite angle are known along with another angle.
How do I use the law of sines side calculator?
Enter known side, angle opposite known side (degrees), angle opposite required side (degrees). The result updates automatically. Use the units shown beside each input; the example values illustrate the method.
Which formula does this calculator use?
Required side = known side × sin(required angle)/sin(known angle).
What should I check before using the result?
The two angles must add to less than 180° so a third positive angle exists.
How are results rounded?
Scalar numbers display up to six decimal places, with scientific notation for very large or small values. Text, fraction, date and schedule outputs use the format described on the tool. Intermediate calculations use JavaScript floating-point arithmetic. Keep sensible precision for your measurements.
Further reading
For background on this topic, see OpenStax: basic functions and identities ↗. This is a topic reference, not an external review or endorsement of this tool.
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