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 \(ABC\), \(A=52^\circ\), \(B=71^\circ\) and \(a=8.4\) cm. Find \(b\).
- \(\dfrac{b}{\sin71^\circ}=\dfrac{8.4}{\sin52^\circ}\)
- \(b=\dfrac{8.4\sin71^\circ}{\sin52^\circ}\)
Answer: \(b=10.1\) 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 |
|---|---|
| AA SL | In the IB formula booklet |
| AI SL | In the IB formula booklet |
| AA HL | In the IB formula booklet |
| AI HL | In the IB formula booklet |
From our own IB Maths formula sheets, in our words. The IB gives its booklet to schools, so we checked against our own copy: your teacher has the official one. Official: IB DP Mathematics page.
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?
AA SL: in the IB formula booklet. AI SL: in the IB formula booklet. AA HL: in the IB formula booklet. AI HL: in the IB formula booklet. This comes from our own IB 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 IB Math Revision. Not produced or endorsed by the International Baccalaureate Organization.