Triangles come up a lot in GCSE mathematics. And there are a variety of different methods that can be applied to questions. If you are given a triangle with a missing side or angle, there are four different methods that you can use to find the missing information (bold means examinable in higher tier only):
- Pythagoras’ Theorem
- Trigonometry (SOHCAHTOA)
- Sine Rule
- Cosine Rule
But how do we know which one to use? In GCSE papers, questions will very rarely say “Use cosine rule to find x” or “Use Pythagoras’ theorem to find y” – you will need to look at the triangle and spot which method to use yourself. In this blog, I will show you a really useful flow chart that will allow you to identify which method is best for the job.
This blog will not work through any examples, it will only determine which method you need to use. So if you need more help with how to use Pythagoras’ Theorem, I recommend reading our guide to Pythagoras’ Theorem. Or if you need more help with trigonometry, you should read our guide to finding missing sides and then our guide to finding missing angles.
Pictured below is my flow chart on how to pick the correct method (click here to open the PDF). Please note that because sine and cosine rule are only on the higher tier syllabus and not the foundation, if you are studying for foundation GCSE maths the right-hand side of the flow chart will not apply so you can ignore that. Also, some triangles will be solvable using more than one of these methods, but the purpose of this flow chart is to pick the easiest method.
First thing to note is that a right angle does not count as a labelled angle, and if an angle is labelled x (or any letter) then this counts as being labelled.
For example, in these two triangles one angle is labelled:
In this triangle, two angles are labelled:
But in this triangle an angle is not labelled:
Now let’s look at some examples to show how the flow chart works.
Example 1
Find x.
Let’s work through the flow chart…
Is it a right-angled triangle? YES
Is an angle labelled? YES
So we need to use SOHCAHTOA.
Example 2
Find y.
Is it a right-angled triangle? NO
Are two angles labelled? YES
So we need to use Sine Rule.
Example 3
Find a.
Is it a right-angled triangle? YES
Is an angle labelled? NO
So we need to use Pythagoras.
Example 4
Find b.
Is it a right-angled triangle? NO
Are two angles labelled? NO
So we need to use Cosine Rule.
Example 5
Find the size of angle ACB.
Now, in this question, there is no angle labelled. But we need to find an angle. So let’s label the angle we need to find as x.
Is it a right-angled triangle? NO
Are two angles labelled? NO
So we have to use Cosine Rule.
Example 6
Find the size of angle EDF.
Same again here, always label any side or angle that you are being asked to find.
Is it a right-angled triangle? YES
Is an angle labelled? YES
So we have to use SOHCAHTOA.
If you want to practice using this flow chart, you can try our miscellaneous triangles worksheets – higher or foundation.
Or, if you want to practice Pythagoras, you can try our worksheet.
If you want to practice trigonometry, you can try our worksheet.
If you want to practice sine and cosine rules, you can try our worksheet.
If you need someone to explain this in person, book in a free taster session.