Pythagoras (GCSE)
GCSE-level Pythagoras: 2D, then 3D (Higher). Always identify the hypotenuse first.
Foundation tier: 2D Pythagoras. Higher: 3D Pythagoras using the diagonal of a cuboid (find a face diagonal first, then use that with the height). Distance between two coordinates uses Pythagoras on the differences.
Worked examples
Triangle 9, 12, c: c² = 81 + 144 = 225 ⇒ c = 15.
Distance from (1, 2) to (4, 6): √((3)² + (4)²) = 5.
Cuboid 3×4×12: face diag = √25 = 5; full = √(25 + 144) = 13.
Frequently asked questions
Pythagorean triples for GCSE?
(3,4,5), (5,12,13), (8,15,17), (7,24,25), (9,40,41) — recognising these saves time in exams.
Always longest side?
Yes — the hypotenuse is opposite the right angle and is always the longest of the three.