Welcome to Advanced Trigonometry. You've probably used SOHCAHTOA to solve problems with right-angled triangles. But what about all the other triangles? In this deck, you'll learn three powerful tools that work for any triangle: the Sine Rule, the Cosine Rule, and a formula for the area. These are usually given to you in the exam, so our focus will be on understanding what they do and when to use them.

First, we need a consistent way to label triangles. We label the angles with capital letters, like A, B, and C. The side opposite each angle is then labelled with the matching lowercase letter. So, the side opposite angle A is side a, the side opposite angle B is side b, and so on. This convention is essential for using the formulas correctly.

Let's start with the area. The formula for the area of any triangle is 'Area equals one half a b sine C'. This means the area is half the product of two sides, multiplied by the sine of the angle between them. The most important part is that the angle, C, must be the 'included angle' – the one squashed between the two sides you are using, a and b.