Pythagoras' theorem in context | Maths | Quizalize & Oak National Academy

Starter quiz

Izzy writes down a correct Pythagoras' theorem equation for a triangle. Which of the three sides of this triangle is the hypotenuse?

side A ✓

side B

side C

impossible to tell
Aisha rearranges a correct Pythagoras' theorem equation for a triangle. Which of these statements are correct?

The hypotenuse of the triangle is side W

The hypotenuse of the triangle is side X

The hypotenuse of the triangle is side Y ✓

Side W has length of 32 400 units.

Side W has a length of 180 units. ✓
Which of these are correct for this triangle?

$20^2 + a^2 = 17^2$

$20^2 = a^2 + 17^2$ ✓

$a^2 = 20^2 - 17^2$ ✓

$a = 10.5$ (to 1 d.p.) ✓

$a = 26.4$ (to 1 d.p.)
What is the value of $b$ , rounded to 2 d.p.? $b=$ ______.

'26.38' ✓
The diagonals of this kite have been drawn on. The value of $x$ is ______.

'8' ✓
The diagonals of this kite have been drawn on. Which of these statements are correct.

The two diagonals of a kite intersect to create two acute angles of equal length

The two diagonals of a kite intersect at right angles ✓

$a° = 38°$ ✓

$a° = 69°$

$a° = 73°$

Exit quiz

On this football pitch, the goalkeeper (at point A) wants to kick the ball to a striker (at point E), however the goalkeeper's longest kick is 91 m. Which of these statements are correct?

The distance between the goalkeeper and the striker is 49.24 metres.

The distance between the goalkeeper and the striker is 92.20 metres (to 2 d.p.). ✓

The distance between the goalkeeper and the striker is 98.49 metres (to 2 d.p.).

The ball the goalkeeper kicks will reach the striker.

The ball the goalkeeper kicks will not reach the striker. ✓
A factory produces cylindrical saucepans whose maximum base length is 28 cm. What must the minimum integer height of the saucepan be (in cm) so it can fully submerge a spaghetti noodle.

15 cm

16 cm ✓

19 cm

28 cm

32 cm
An archer fires an arrow that travels 20 metres to hit a target that is 9 m above ground. The arrow then drops to the ground. The archer must walk ______ m (to 2 d.p.) to pick up the arrow.

'17.86' ✓
An archer fires an arrow at a target 20 m away. The arrow drops 9 m to the ground. Jun uses Pythagoras' theorem to find how far the archer walks to collect the arrow. What assumptions does Jun make?

The arrow travels in a straight line. ✓

The speed of the arrow is constant.

The ground the archer walks on to pick up the arrow is flat. ✓

The archer fires the arrow from the ground. ✓

The accuracy of the archer.
The captain (at C) passes the ball to the goalkeeper (at A), who then passes to the midfielder (at D), who then passes to a striker (at F). The total distance the ball travelled is ______m (to 2 d.p.).

'154.45' ✓
Two bamboo sticks are placed on the diagonal of this kite to support it during high winds. The length of the vertical bamboo stick is ______ cm (to 2 d.p.).

'189.29' ✓

Worksheet

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Lesson Details

Key learning points

Within context, it can be difficult to initially identify whether Pythagoras' theorem can be used.
Pythagoras' theorem may be used if a right-angled triangle can be drawn, even if drawn within a different shape.
Pythagoras' theorem can be used to check for properties of other shapes involving right-angles.

Common misconception

I need to be given a triangle in order to use Pythagoras' theorem.

You do not need to be given a triangle. It is an important skill to be able to sketch and label a triangle for yourself from given information, or go straight into an algebraic stage of calculation if aware that lengths given are perpendicular.

Keywords

Perpendicular height - The perpendicular height is the perpendicular distance from the base to the opposite vertex.
Pythagoras’ theorem - Pythagoras’ theorem shows that the sum of the squares of the two shorter sides of a right-angled triangle is equal to the square of its longest side (the hypotenuse).
Hypotenuse - A hypotenuse is the side of the right-angle triangle which is opposite the right-angle.