Did you know that the word trigonometry comes from ancient Greek?

'Trigonon' was their word for triangle and 'metron' their word for measure.

Trigonometry - measuring triangles, sounds simple then!

**"SOH, CAH, TOA"** is something that every maths teacher has probably chanted at you.

We are going to look at **Cos** here and what the **"CAH"** means.

A formula triangle is helpful:

C is for Cos (which will be given as an angle)

A is for adjacent side

H is the hypotenuse side

The line in the middle means divide.

To use this triangle we cover up what side it is we want to find and we are left with a formula to follow.

If we want to find the adjacent side, cover up the A. The formula we are left with is Cos(angle) x Hypotenuse.

If we want to find the hypotenuse, cover up the H. The formula we are left with is adjacent (A) divided by Cos(angle)

Let's look at some examples.

**IMPORTANT NOTE:** Make sure your calculator is set to **degrees **otherwise this formula will not work correctly. (If you are in the right mode, you should see a "D" at the top of the calculator screen).

**Example 1**

Find length x in this triangle.

1. Label the lengths of the triangle: **A**, **O**, and **H**

2. Work out the side you want to find. In this case, x is the adjacent length, so we want **A**

3. The formula triangle shows that **A** = **C** x **H**

4. Substitute the angle and the length into the formula. This gives **A** = cos47 x 7

5. In your calculator type in cos 47 x 7

6. Your answer should be 4.77 cm to 2 decimal places.

**Example 2**

Find length x in this triangle.

1. Label the lengths of the triangle: **A**, **O**, and **H**

2. Work out the side you want to find. In this case, x is the hypotenuse, so we want **H**

3. The formula triangle shows that **H** = **A **÷ **C**

4. Substitute the angle and the length into the formula. This gives **H** = 15 ÷ cos32

5. In your calculator type 15 ÷ cos32

6. Your answer should be 17.69 cm correct to 2 decimal places

Now that you have seen the formula and how to use it, have a go at 10 questions!