What do the following have in common?

A triangle, a tricycle, a triathlete, trigonometry.

Answer: The number ** three**. There are three sides on a triangle, three wheels on a tricycle, three events in a triathlon and three ratios to learn in trigonometry.

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

We are going to look at **Sin** here and what the **"SOH"** means.

A formula triangle is helpful:

**S** is for sin (which will be given as an angle)

**O** is for opposite side

**H** is the hypotenuse side

The line in the middle means divide.

If we want to find the hypotenuse, cover up the H. The formula we are left with is **H = O/S**

Hypotenuse = opposite divided by Sin(angle)

If we want to find the opposite side, cover up the O. The formula we are left with is **O = S x H**

Opposite = sin(angle) x Hypotenuse.

** IMPORTANT NOTE:** Make sure your calculator is set to

__, otherwise the calculation will not work. You can tell you are in the right mode as a "D" should appear at the top of your calculator screen.__

**degrees**__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 hypotenuse, so we want H

3. The formula triangle shows that H = O / S

4. Substitute the angle and the length into the formula. This gives H = 12 / sin(32)

5. In your calculator type in 12 / sin(32)

6. Your answer should be 22.64 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 opposite, so we want O

3. The formula triangle shows that O = S x H

4. Substitute the angle and the length into the formula. This gives O = sin(47) x 11

5. In your calculator type in sin(47) x 11

6. Your answer should be 8.04 cm to 2 decimal places.

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