# Year 9 Maths Chapter 3 - Right-angled triangles

## “the earth is flat” – our Year 9 maths teacher

*You will want to refer to Year 8 Maths Chapter 6 for basic geometry. This section is more advanced, and omits basic concepts.*

#### Table of Contents

## Pythag

```
a² + b² = c²
```

where `a`

and `b`

is the opposite/adjacent, and `c`

is the hypotenuse

Pythagorean triads include 3, 4, 5 (because `3² + 4² = 5²`

) and 6, 8, 10 (because `6² + 8² = 10²`

).

## Trig ratios

Take a right angled triangle with angle `θ`

.

- The longest side of the triangle (opposite the right angle) is the
**hypotenuse**. - The side opposite
`θ`

is the**opposite**. - The side adjacent to
`θ`

is the**adjacent**.

There are trig ratios for these sides: sine, cosine, and tangent, which are abbreviated to `sin`

, `cos`

and `tan`

respectively.

In all of the below ratios, the side in the ratio refers to the length of a corresponding side. E.g opposite over adjacent = length of opposite side over length of adjacent side.

- Sine ratio
`opposite sinθ = –––––––––– adjacent`

- Cosine ratio
`adjacent cosθ = –––––––––––– hypotenuse`

- Tangent ratio
`opposite tanθ = –––––––––– adjacent`

This can be remembered using the term:

### SOH CAH TOA

### Finding sides

More on Finding Sides at Khan Academy

- Find trig ratio
- With the trig ratio, replace θ with the (acute) angle stated
- Insert a pronumeral for the unknown side, into the trig ratio
- Solve

### Finding angles

- Find trig ratio
- Insert the appropriate sides into their corresponding positions on the trig ratio
- Use sin⁻¹(your ratio here) to solve for the unknown angle

## Angles of elevation and depression

More at Khan Academy on Angles of Elevation and Depression

- The angle of
**elevation**is how big the angle between a horizontal and a line of sight is. e.g when you look up, you are forming an angle of elevation - Similarly, the angle of
**depression**is how big the angle between a horizontal and line of sight is, but instead of being up, it is down

oof that meme

## Bearing

Measured clockwise from north