# Introductory Trigonometry

How are heights of mountains measured? Mountain climbers do not carry tape measures. Mathematics called **trigonometry** is used.
The word "trigonometry" has three parts - "tri" means "three", "gon" means "shape", and "metry" means "measure".
We will use rules to calculate the side lengths and the angles of **right-angled triangles**.

## Parts of a Right-Angled Triangle

**Right angle** - In a right-angled triangle, there is always a right angle or 90°.

**Angle θ** - the angle in which we are interested; uses the Greek letter "theta" which is the equivalent of the English letter "T"

**Hypotenuse** - the side opposite the right angle

**Opposite side** - the side opposite angle; the side all the way across the triangle from angle θ

**Adjacent side** - the side adjacent angle θ; the side next door to angle θ

## Did You Know That...?

What is the world's highest mountain?

If you said **Mount Everest in Nepal**, you would be correct for the highest mountain above sea level.

If you said **Mount Chimborazo in Ecuador** (see picture above), you would be correct for the mountain furthest from the centre of the Earth.

## Example - Parts of a Right-Angled Triangle

In the following right triangle, which are the Hypotenuse, the Opposite side and the Adjacent side?

**Mark these with H, O and A.**

**Answer:**

## 3 Trigonometry Ratios or Rules

Sin θ = | Opposite side |

Hypotenuse |

Cos θ = | Adjacent side |

Hypotenuse |

Tan θ = | Opposite side |

Adjacent side |

Where **sin**, **cos** and **tan** are abbreviations for mathematical operations called **sine**, **cosine** and **tangent**.

## Did You Know That...?

For brevity, the three trigonometry rules are abbreviated even further to:

**Sin θ = O/H**
**Cos θ = A/H**
**Tan θ = O/A**

A **mnemonic** to remember these rules is "**S**ome **O**ld **H**ags **C**an't **A**lways **H**ide **T**heir **O**ld **A**ge" or "**SOH-CAH-TOA**".

## Question

To learn the three trigonometry rules, make up a **mnemonic** of your own.