GCSE · Pythagoras & right-angled trigonometry

Pythagoras' theoremExam-style questions

Why a² + b² = c² holds, spotting the hypotenuse, the add-or-subtract decision, testing whether a triangle is right-angled, distance between two coordinates, and Pythagoras in 3D.

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13 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4 Level 5

1
The diagram shows a right-angled triangle.Diagram NOT accurately drawn

(a) Work out the length of the hypotenuse. (2 marks)

(b) Work out the area of the triangle. (1 mark)
Level 2 · 3 marksTry it
2
$ABC$ is a right-angled triangle.Diagram NOT accurately drawn

$AB = 7.4$ cm and $BC = 5.9$ cm.

Work out the length of $AC$ .

Give your answer correct to 1 decimal place. (3 marks)
Level 2 · 3 marksTry it
3
$A$ is the point $(-2, 3)$ and $B$ is the point $(4, 11)$ .

(a) Work out the length of $AB$ . [3]

(b) Work out the gradient of the line $AB$ . [1]
Level 2 · 4 marksTry it
4
The diagram shows a right-angled triangle.Diagram NOT accurately drawn

Work out the length of $x$ .
Level 2 · 3 marksTry it
5
The diagram shows a right-angled triangle.Diagram NOT accurately drawn

Work out the value of $x$ .
Level 2 · 2 marksTry it