Sine rule
a/sin A = b/sin B = c/sin C. For non-right-angled triangles. Higher tier.
Use when you have a side and its opposite angle, plus another side or angle. Rearrange the formula to find the unknown. The ambiguous case (two possible angles) is rare but examinable.
Worked examples
A = 30°, a = 5, B = 70°: b = 5 sin 70 / sin 30 ≈ 9.40.
a = 7, A = 40°, b = 8: sin B = 8 sin 40 / 7 ≈ 0.735 ⇒ B ≈ 47.3°.
Sum of angles in a triangle = 180°. Useful for finding the third angle.
Frequently asked questions
When sine rule vs cosine rule?
Sine rule: side + opposite angle pair. Cosine rule: three sides, or two sides and the included angle.
Ambiguous case?
If sin B is between 0 and 1 there are two possible angles (e.g. 47.3° and 132.7°). Check the context to pick the right one.