Law of Sines Calculator
Solve triangles using the Law of Sines: a/sin(A) = b/sin(B) = c/sin(C). Find unknown sides and angles in any triangle when you know two angles and a side (AAS/ASA) or two sides and an angle (SSA).
Formula & Reference
| Variable | Symbol | Formula | Units |
|---|---|---|---|
| Law of Sines Calculator | — | a/sin(A) = b/sin(B) = c/sin(C) | sides and degrees |
Step-by-Step Examples
a=7, A=40°, B=60°.
- C=180−40−60=80°
- ratio=7/sin(40°)=10.89
- b=10.89×sin(60°)=9.43
- c=10.89×sin(80°)=10.73
a=7, A=40°, b=5.
- sin(B)=5/7×sin(40°)=0.4592
- B=arcsin(0.4592)≈27.3°
- C=112.7°, c≈10.07
a=10, A=30°.
- Ratio=10/sin30°=10/0.5=20
- If b=15: sin(B)=15/20=0.75, B≈48.6°
Real-World Applications
Common Mistakes to Avoid
Two sides and a non-included angle may give 0, 1, or 2 valid triangles. Check if sin(B)>1 (no solution) and whether two angles are possible.
Use sines for AAS, ASA. Use cosines for SAS, SSS. For SSA, check which applies.
After finding two angles, verify the third: C=180−A−B. If any angle is ≤0°, no valid triangle exists.
Frequently Asked Questions
Related Math Calculators
Formula Explorer connections
Interpretation: This relationship connects dimensions, coordinates, angles or trigonometric ratios to a geometric measurement. Assumption: Use a consistent angle mode and length unit, identify the intended shape or coordinate system, and verify that the supplied dimensions form valid geometry.