Maths Library

Pythagoras' Theorem: Year 13 maths

This topic covers applying Pythagoras' theorem to find unknown side lengths in right-angled triangles. The worksheet practises calculating the hypotenuse, finding a shorter leg, and solving simple applied context problems.

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What this covers

Pythagoras' Theorem is taught in Year 13 (age 17 to 18, KS5) as a topic to introduce. It sits in the Geometry strand.

Worked example

A right-angled triangle has shorter sides of length 6 cm and 8 cm. Calculate the length of the hypotenuse c.

  1. State Pythagoras' theorem: a^2 + b^2 = c^2
  2. Substitute side lengths: 6^2 + 8^2 = 36 + 64 = 100
  3. Take the square root: c = sqrt(100) = 10

Answer: 10

Difficulty scale

The sheet generator offers five difficulty settings for this topic.

  1. Calculating hypotenuse using Pythagorean triples with whole number answers
  2. Calculating a shorter leg with whole number answers
  3. Finding hypotenuse requiring square root rounding to 1 decimal place
  4. Finding shorter leg requiring rounding to 1 decimal place
  5. Multi-step word problems or finding distance between coordinate points

Common mistakes

  • Adding side lengths before squaring instead of squaring first
  • Adding squares when calculating a shorter side instead of subtracting

Curriculum links

Indicative matches to National Curriculum for England. Check wording and codes against the official document.

  • Utilise Pythagoras' theorem to calculate magnitudes and distances in three-dimensional Cartesian coordinate systems.

Sample sheet and answers

Six questions at the level's usual difficulty. Open the editor to change, add or regenerate any of them.

Pythagoras' Theorem

Year 13 maths

Qs
6
Marks
24
NameDateScore / 24
1.
A right-angled triangle has hypotenuse 15 cm and one side 9 cm. Find the other side.
[4]
2.
A right-angled triangle has hypotenuse 13 cm and one side 5 cm. Find the other side.
[4]
3.
A right-angled triangle has hypotenuse 17 cm and one side 8 cm. Find the other side.
[4]
4.
A right-angled triangle has hypotenuse 17 cm and one side 8 cm. Find the other side.
[4]
5.
A right-angled triangle has hypotenuse 17 cm and one side 8 cm. Find the other side.
[4]
6.
A right-angled triangle has shorter sides 3 cm and 4 cm. Find the hypotenuse.
[4]

Answer key

  1. 12 cmb2 = 152 − 92 = 225 − 81 = 144; b = 12 cm
  2. 12 cmb2 = 132 − 52 = 169 − 25 = 144; b = 12 cm
  3. 15 cmb2 = 172 − 82 = 289 − 64 = 225; b = 15 cm
  4. 15 cmb2 = 172 − 82 = 289 − 64 = 225; b = 15 cm
  5. 15 cmb2 = 172 − 82 = 289 − 64 = 225; b = 15 cm
  6. 5 cmc2 = 32 + 42 = 9 + 16 = 25; c = 5 cm