Free · Mathematics models
Paired Triangle Sides by the Sine Rule
Solve each captured side-angle pair and inspect a valid supplementary-angle alternative in the SSA case.
- Formula & worked example
- Private in your browser
- No signup
Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
Private by default
Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.
Formula and method
With side a=3, alpha=30 degrees and beta=90 degrees, side b=6.
a/sin(alpha)=b/sin(beta)=c/sin(gamma).
Worked example
Enter these known values and leave the other values blank.
- Side a
- 3 cm
- Angle α
- 30 deg
- Angle β
- 90 deg
- Side b
- 6 cm
Assumptions and limitations
- Select the paired ratio to solve. Angles opposite sides must be strictly positive and less than 180 degrees; any two triangle angles sum to less than 180 degrees.
- An inverse sine initially returns the principal angle. A supplementary alternative is a distinct triangle only when the known angle plus the supplementary angle is less than 180 degrees.
- The captured pair-wise tool does not independently enforce a three-angle sum when all angles are manually supplied; use its consistency checks and the triangle angle sum before interpreting a complete triangle.
- Clear the unknown numerical field before using a supported inverse; selection controls retain their captured branches.
Common questions
What assumptions matter for this model?
Select the paired ratio to solve. Angles opposite sides must be strictly positive and less than 180 degrees; any two triangle angles sum to less than 180 degrees.
What does this model leave out?
The captured pair-wise tool does not independently enforce a three-angle sum when all angles are manually supplied; use its consistency checks and the triangle angle sum before interpreting a complete triangle.
References
Model requirements: Side a must be positive. Side b must be positive. Side c must be positive. Authored accessible explanations preserve each captured diagram mode and its geometric relationships. Replace the pinned dimensionally invalid ambiguity test comparing a side length with an angle by the supplementary-angle triangle criterion; retain every paired sine-rule equation and inverse, and all three alternative-angle outputs.