Maths Library

Pythagorean Theorem: Grade 10 math

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

Pythagorean Theorem is taught in Grade 10 (age 15 to 16) 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 Common Core State Standards. Check wording and codes against the official document.

  • Apply the Pythagorean theorem and trigonometric ratios to solve right triangles in applied contexts.

Sample sheet and answers

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

Pythagorean Theorem

Grade 10 math

Qs
6
Marks
18
NameDateScore / 18
1.
A right-angled triangle has hypotenuse 15 cm and one side 9 cm. Find the other side.
[3]
2.
A right-angled triangle has hypotenuse 13 cm and one side 5 cm. Find the other side.
[3]
3.
A right-angled triangle has hypotenuse 17 cm and one side 8 cm. Find the other side.
[3]
4.
A right-angled triangle has hypotenuse 17 cm and one side 8 cm. Find the other side.
[3]
5.
A right-angled triangle has hypotenuse 17 cm and one side 8 cm. Find the other side.
[3]
6.
A right-angled triangle has shorter sides 3 cm and 4 cm. Find the hypotenuse.
[3]

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