# Sine rule

For any triangle, side a over sin A equals side b over sin B. It links sides to the angles opposite them.

Maths (school) · Part 06: Pythagoras and trigonometry · Card 8 of 9 · Last updated 2026-10-19

## Analogy

Like a fair-trade rule: each side always has the same ratio to its opposite angle.

## Example

**A = 30, a = 7, B = 50**

b / sin 50 = 7 / sin 30
b = 7 x sin 50 / sin 30
= 7 x 0.766 / 0.5
= 10.7

## In practice

Navigators use it to find distances when no angle is a right angle.

## Practice

### Flashcards

- **Write the sine rule.** a / sin A = b / sin B.

## Questions people ask

### When do you use the sine rule?

Use it when you know an angle and the side opposite it, plus one more angle or side. You need a matching pair. If you only know two sides and the angle between them, you need the cosine rule instead.

### How does the sine rule go when finding an angle?

Flip the rule so the sines are on top: sin A / a = sin B / b. Substitute what you know, rearrange to find sin of the unknown angle, then use the inverse sine button on your calculator to find the angle.

## Related concepts

- [Sine, cosine and tangent](https://studyvisually.com/learn/science/maths-school/maths-school-part-6/maths-school-part-6-concept-3)
- [Finding a missing side](https://studyvisually.com/learn/science/maths-school/maths-school-part-6/maths-school-part-6-concept-4)
- [Finding a missing angle](https://studyvisually.com/learn/science/maths-school/maths-school-part-6/maths-school-part-6-concept-5)
- [Exact trigonometry values](https://studyvisually.com/learn/science/maths-school/maths-school-part-6/maths-school-part-6-concept-6)

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