Sine rule formula: a/sin A = b/sin B
The sine rule formula is a/sin A = b/sin B = c/sin C.
What each letter means
- \(a,\ b,\ c\) the lengths of the sides
- \(A,\ B,\ C\) the angles opposite those sides (angle A is opposite side a)
When to use it
In a triangle without a right angle, when you know a side and the angle opposite it, plus one more side or angle. To find an angle, use it upside down: sin A / a = sin B / b.
Worked example
In triangle \(PQR\), angle \(P=35^\circ\), angle \(Q=110^\circ\) and \(QR=6\) cm. Find \(PR\).
- \(QR\) is opposite \(P\) and \(PR\) is opposite \(Q\)
- \(PR=\dfrac{6\sin110^\circ}{\sin35^\circ}\)
Answer: \(PR=9.83\) cm (3 s.f.)
Common mistake
Pairing a side with the wrong angle. Each side goes with the angle opposite it, not an angle next to it.
On your course
| Course | In the exam |
|---|---|
| Edexcel 4MA1 (Higher) | On the formulae page of the Higher papers |
| Cambridge 0580 | On the list of formulas in Extended papers (Extended only) |
From our own IGCSE Maths formula sheets, in our words. Official: Pearson's 4MA1 specification (PDF, Appendix 5) · Cambridge's 0580 syllabus (PDF).
Practise and revise
Questions
What is the sine rule formula?
The sine rule formula is a/sin A = b/sin B = c/sin C. a, b, c: the lengths of the sides; A, B, C: the angles opposite those sides (angle A is opposite side a).
Is the sine rule given in the exam?
Edexcel 4MA1 (Higher): on the formulae page of the Higher papers. Cambridge 0580: on the list of formulas in Extended papers (Extended only). This comes from our own IGCSE Maths formula sheets; your teacher has the official booklet.
What is the ambiguous case of the sine rule?
When you find an angle from two sides and an angle that is not between them, there can be two answers: θ and 180° − θ. Both are possible if the second still leaves room for the third angle.
Our own wording, examples and card, checked by IGCSE Math Revision. Not produced or endorsed by Pearson Edexcel.