# Finding a missing side

Put the angle and known side into the correct ratio, then rearrange to get the unknown side.

Maths (school) · Part 06: Pythagoras and trigonometry · Card 4 of 9 · Last updated 2026-10-19

## Analogy

Like a recipe with one missing ingredient: you use the other amounts to work it out.

## Example

**Hypotenuse 10, angle 30**

Opposite is needed, so use sin
sin 30 = opposite / 10
opposite = 10 x sin 30
= 10 x 0.5 = 5

## In practice

Ladder safety: knowing the angle and length tells you how high it reaches.

## Practice

### Flashcards

- **Find the opposite side if the hypotenuse is 10 and the angle is 30.** 5. Opposite = 10 x sin 30 = 10 x 0.5.

## Questions people ask

### Why should your calculator be in degree mode?

Calculators can measure angles in degrees or radians. School questions use degrees. In the wrong mode, sin 30 gives a strange answer instead of 0.5. Check for a small D or DEG on the screen before you start. Test it by pressing sin 90: in degree mode the answer should be exactly 1.

### What if the unknown side is on the bottom of the fraction?

Rearrange so the unknown is on top. For cos 40 = 7 / x, swap them to get x = 7 / cos 40. That is about 9.14. Another way is to multiply both sides by x first, then divide.

## 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 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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