DfE statement G20 · Geometry and measures
Pythagoras’ theorem and trigonometric ratios
Pythagoras’ theorem and trigonometric ratios is content statement G20 of the DfE GCSE mathematics subject content, in the geometry area. It is on both tiers, with a Higher-only part, and it is normally a calculator-paper question. Below is what the specification actually requires, the 4 mistakes that cost marks on this topic most often, and practice questions written to the statement — original questions, not past papers.
What the specification says
The DfE subject content for GCSE mathematics states, verbatim: "Know the formulae for: Pythagoras’ theorem, a² + b² = c², and the trigonometric ratios, sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse and tan θ = opposite/adjacent; apply them to find angles and lengths in right-angled triangles and, where possible, general triangles in two and three dimensional figures." (statement G20). Every awarding organisation — Pearson Edexcel, AQA and OCR — must cover it, so the wording is the same whichever specification your school follows.
Tier
Both tiers, but part of it is Higher only. Foundation covers the statement except for the following, which the DfE prints in bold and reserves for Higher: "and, where possible, general triangles", "and three dimensional figures". Everything else in the statement is Foundation content.
Calculator
This is calculator work, which places it on Papers 2 and 3. Know your own calculator before the exam, keep full accuracy through the working and round only at the end.
Common mistakes
- Adding the squares when finding a shorter side. If c is the hypotenuse, a shorter side comes from c² − b², not c² + b².
- Choosing the wrong ratio: using sine when the sides given are the adjacent and the hypotenuse, which calls for cosine.
- Leaving the calculator in radian mode, which makes every trigonometric answer wrong by an amount that looks plausible.
- Using Pythagoras or the basic ratios on a triangle that is not right-angled.
Formulae for this statement
Sample questions (10 of 30)
Nearby statements
Questions people ask
Is pythagoras’ theorem and trigonometric ratios on Foundation or Higher?
Both, but not all of it. The parts the DfE prints in bold — "and, where possible, general triangles", "and three dimensional figures" — are Higher only; the rest is Foundation content.
Can I use a calculator for pythagoras’ theorem and trigonometric ratios?
Yes, on Papers 2 and 3, which are the calculator papers and where questions on this usually sit. Paper 1 is non-calculator.
How do I know which trigonometric ratio to use?
Label the sides relative to the angle you know or want: opposite, adjacent and hypotenuse. Then pick the ratio containing the two sides in play — sine is opposite over hypotenuse, cosine is adjacent over hypotenuse, tangent is opposite over adjacent. If the triangle has no right angle, you need the sine or cosine rule instead, which are Higher tier.
What is the single most common mistake here?
Adding the squares when finding a shorter side. If c is the hypotenuse, a shorter side comes from c² − b², not c² + b².
Are these past paper questions?
No. Every question is original, written to this DfE content statement and checked before publication. We do not host past papers or mark schemes.
Back to Geometry and measures at Foundation or at Higher.