Great, this is what we have been waiting for. Time to top up the tan!

Okay so maybe not that sort of "tan".

We can use the **tan ratio** to help us find a missing side length in a **right angled triangle.**

We are going to look at Tan here and what the "TOA" means.

A formula triangle is helpful:

T is for Tan (which will be given as an angle)

A is for adjacent side

O is the opposite 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 opposite side, cover up the O. The formula we are left with is Tan(angle) x Adjacent.

**O = T x A**

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

**A = O ÷ T**

Let's look at some examples.

**IMPORTANT NOTE: **Make sure your calculator is set to degrees otherwise this formula will not work correctly. (You should see a D at the top of the calculator screen if it is in the correct mode).

**Example 1**

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 opposite length, so we want O

3. The formula triangle shows that O = A x T

4. Substitute the angle and the length into the formula. This gives O = 7 x tan47

5. In your calculator type in 7 x tan 47

6. Your answer should be 7.51 cm to 2 decimal places.

**Example 2**

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 = O ÷ T

4. Substitute the angle and the length into the formula. This gives A = 15 ÷ tan 32

5. In your calculator type in 15 ÷ tan 32

6. Your answer should be 24.00 cm to 2 decimal places.