Sine and Cosine Rules

Normal trigonometry using SOH CAH TOA etc. can only be applied to right-angled triangles. For non right-angled triangles we use the Sine and Cosine rules.

Step 1: Labelling the Triangle

Here is how you should label your triangles. It doesn't matter which side you call a, b, and c (as long as the angles are labelled properly). Also, which ever angle you label 'A' you must label the opposite side 'a'.

Step 2: Choosing Which Formula to Use

The Sine Rule

Please note that you don't use the whole thing with both '=' signs. You just choose the two parts you want, depending on how you have labelled your triangle.

The Cosine Rule
There are two forms. The 'normal' form is:

The form for finding and angle is:

Please note that you do not have to memorise this formula. You can simply rearrange it from the formula you are given in the front of your maths paper.

Area of a Triangle
This formula is used when you know two sides and the angle between them:

If you use this formula then it is easiest if you label the angle that you are given 'C' so you can easily substitute it into the formula.

Please also note that you already know a simple formula for calculating the area which is 1/2(base x height). The formula here is used for when you don't have those values.

Thank you for reading this blog post. My next post will be Sine and Cosine rule worked examples.
Amelia