# Sine, cosine and tangent

Three ratios linking an angle in a right-angled triangle to its sides: sin = opposite / hypotenuse, cos = adjacent / hypotenuse, tan = opposite / adjacent.

Maths (school) · Part 06: Pythagoras and trigonometry · Card 3 of 9 · Last updated 2026-10-19

## Analogy

SOH CAH TOA is a chant that reminds you which sides go with which ratio.

## Example

**Labelling the sides**

Hypotenuse: opposite the right angle
Opposite: facing your angle
Adjacent: next to your angle
Use SOH CAH TOA to pick the ratio

## In practice

Surveyors use them to find heights and distances they cannot measure directly.

## Practice

### Flashcards

- **What does SOH stand for?** Sine = Opposite / Hypotenuse.

## Questions people ask

### How do you choose between sin, cos and tan?

Label the sides: hypotenuse, opposite and adjacent. Then see which two sides you have or need. If they are opposite and hypotenuse, use sin. If adjacent and hypotenuse, use cos. If opposite and adjacent, use tan. Writing SOH CAH TOA at the top of your working is a good habit under exam pressure.

### Does trigonometry only work for right-angled triangles?

The basic SOH CAH TOA ratios only work in right-angled triangles. For other triangles you can use the sine rule and cosine rule, which are covered later, or split the triangle into two right-angled ones. Many real problems become right-angled once you draw a helpful vertical line.

## Related concepts

- [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)
- [Angles of elevation and depression](https://studyvisually.com/learn/science/maths-school/maths-school-part-6/maths-school-part-6-concept-7)

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