The Cosine Rule can be used in any triangle where you are trying to relate all three sides to one angle.
If you need to find the length of a side, you need to know the other two sides and the opposite (or ‘included’) angle. You need to use the version of the Cosine Rule where a2 is the subject of the formula:
You will be given this formula in your GCSE exam. Side a is the one you are trying to find. Sides b and c are the other two sides, and angle A is the angle opposite side a.
If you need to find the size of an angle, you need to use the version of the Cosine Rule where the cos(A) is on the left:
You will have to rearrange the first formula to get this one.
Remember - in case you make a mistake when using your calculator, write out your stages of working clearly.
If you need more explanation of the Cosine Rule, look at the lessons on MyMaths (under shape>trigonometry) or come and see me. Here’s our worksheet from the lesson, including answers.
Here’s an extension question for you to try: Two ships leave port at 13.00. Ship A travels on a bearing of 075o at a speed of 12 kilometres per hour. Ship B travels on a bearing of 110o at a speed of 30 kilometres per hour. How far apart are the ships at 15.30?
The answer is 53.3km – did you get it? :)