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 with hypotenuse $25$ cm.Diagram NOT accurately drawn

(a) Work out the length of $y$ .

(b) Work out the distance between the points $(-3, 2)$ and $(5, 8)$ .
Level 3 · 5 marksTry it
2
A ladder leans against a vertical wall. The foot of the ladder is $1.4$ m from the base of the wall, and the ladder reaches $4.2$ m up the wall.Diagram NOT accurately drawn

Work out the length of the ladder. Give your answer correct to 1 decimal place.
Level 3 · 3 marksTry it
3
(a) A triangle has sides of length $8$ cm, $15$ cm and $17$ cm. Show that this triangle is right-angled.

(b) A different triangle has sides of length $7$ cm, $9$ cm and $12$ cm. Determine whether this triangle is right-angled. You must show your working.
Level 3 · 4 marksTry it
4
A right-angled triangle has hypotenuse $41$ cm and one shorter side of length $40$ cm.

Work out the length of the third side.
Level 3 · 2 marksTry it
5
$A$ is the point $(1, 2)$ and $B$ is the point $(7, 10)$ .

Work out the length of the line segment $AB$ .
Level 3 · 3 marksTry it