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Year 9 · Shapes & Geometry

Pythagoras: find a shorter side

In a right-angled triangle, the two short sides squared add up to the longest side squared: a² + b² = c².

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How to do it

  1. Square the two sides you know.
  2. Finding the hypotenuse: add, then square root.
  3. Finding a short side: subtract, then square root.

Worked example

Hypotenuse 5, one short side 4
5² − 4² = 25 − 16 = 9
√9 = 3

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The hypotenuse is always opposite the right angle and always the longest.

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