Pearson Edexcel International GCSE Mathematics · specification 4MA1 · Paper 1F | Whole paper: Number, Algebra, Geometry, Statistics · Free · no account needed
Pythagoras' theorem and trigonometry (4MA1 specification)
Finding missing sides and angles in right-angled triangles, and — at Higher — in any triangle at all.
Learn it on Incandio
The 8 Incandio pages that teach this — each explained in full, then proved in marked questions, taught back to an AI pupil and defended in a debate. Completely free.
- Angles & Parallel Lines — Angle facts on lines, at points and between parallels — and the exam habit that doubles your marks: naming the reason for every step.
- Perimeter & Area — Rectangles, triangles, parallelograms, trapezia and compound shapes — with the height rule that separates area marks from area guesses.
- Circles, Arcs & Sectors — Circumference and area, then the fraction-of-a-circle thinking that turns arcs and sectors into one idea instead of four formulas.
- Volume & Surface Area — Prisms, cylinders, spheres and cones — filling solids (volume) and wrapping them (surface area), including the formulas the sheet won't give you.
- Pythagoras' Theorem — a² + b² = c² — finding missing sides in right-angled triangles, and spotting the hidden right triangles inside other shapes.
- Right-Angled Trigonometry — Sine, cosine and tangent: finding sides and angles in right triangles, from ladders to angles of elevation — plus the exact values worth knowing.
- The Sine & Cosine Rules — Trigonometry escapes the right angle: solving ANY triangle, plus the ½ab sin C area formula. Higher Tier.
- 3-D Pythagoras & Trigonometry — Space diagonals, angles between lines and planes — finding the flat right-angled triangle hiding inside every solid. Higher Tier.
The teaching routes these belong to: Geometry · Mensuration · Trigonometry — the lessons in order, with every gate.
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.
This page maps the specification. The pages above teach it, and the Mathematics modules hold the whole course — completely free.