# Finding a missing angle

Use the inverse button (sin^-1, cos^-1 or tan^-1) on your calculator to turn a ratio back into an angle.

Maths (school) · Part 06: Pythagoras and trigonometry · Card 5 of 9 · Last updated 2026-10-19

## Analogy

Like running a machine backwards: it took an angle in, now you give the answer and get the angle out.

## Example

**Opposite 3, adjacent 4**

tan(angle) = 3 / 4 = 0.75
angle = tan^-1(0.75)
= 36.9 degrees

## In practice

A ramp designer finds the slope angle from the height and length.

## Practice

### Flashcards

- **Find the angle if opposite = 3 and adjacent = 4.** 36.9 degrees, from tan^-1(0.75).

## Questions people ask

### What does tan^-1 mean?

It is the inverse tangent. It does the opposite job to tan. If tan of an angle is 0.75, then tan^-1(0.75) gives you the angle, 36.9 degrees. It is not the same as 1 divided by tan. On most calculators you reach it by pressing the shift or second function key first.

### How do you know whether to use sin^-1, cos^-1 or tan^-1?

Pick the ratio using SOH CAH TOA, based on the two sides you know. Then use the inverse of that same function. If you know the opposite and adjacent sides, you use tan, so you press tan^-1 on the calculator.

## 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)
- [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)

Web page: https://studyvisually.com/learn/science/maths-school/maths-school-part-6/maths-school-part-6-concept-5
Study this card in the app: https://studyvisually.com/app/learn?category=maths-school&card=maths-school-part-6-concept-5