Pythagoras' theorem and trigonometry
Pearson Edexcel International GCSE Mathematics · 4MA1
Paper 1F | Whole paper: Number, Algebra, Geometry, Statistics
Finding missing sides and angles in right-angled triangles, and — at Higher — in any triangle at all.
Specification coverage
4 Geometry and trigonometry — statements 4.7–4.10 (Foundation and Higher Tier)
Assessment objectives: AO2. Suggested learning time: 110 minutes.
Required knowledge
- Know, understand and use Pythagoras' theorem in two dimensions
- Use sine, cosine and tangent to find sides and angles in right-angled triangles
- Higher: the sine rule, the cosine rule and the area of a triangle as ½ab sin C
- Higher: Pythagoras and trigonometry in three dimensions
- Angles of elevation and depression, and bearings
Required skills
- Decide between Pythagoras and trigonometry from what is given
- Choose the correct ratio by labelling opposite, adjacent and hypotenuse first
- Choose between the sine and cosine rules from the information available (Higher)
How it is examined
- Structured questions building from a routine start to a multi-step finish
- Problem-solving questions with no method given
- 'Show that' and reasoning questions where the working IS the answer
Common mistakes
- Using Pythagoras to find an angle. Pythagoras finds sides only.
- Labelling the hypotenuse as the longest side drawn rather than the side opposite the right angle.
- Forgetting to use the inverse function when finding an angle, and giving a ratio as if it were degrees.
- Rounding mid-calculation, which shifts a final angle by a whole degree.