Pythagoras' Theorem

5 minQuiz at the end

Pythagoras' Theorem

In any right-angled triangle:

aΒ² + bΒ² = cΒ²

Where c is the hypotenuse (the side opposite the right angle β€” always the longest side), and a and b are the other two sides.

Finding the Hypotenuse

Sides = 3cm and 4cm:

  • cΒ² = 3Β² + 4Β² = 9 + 16 = 25
  • c = √25 = 5cm

Finding a Shorter Side

Hypotenuse = 13cm, one side = 5cm:

  • 5Β² + bΒ² = 13Β²
  • 25 + bΒ² = 169
  • bΒ² = 144
  • b = 12cm

Pythagorean Triples

Sets of whole numbers that satisfy aΒ² + bΒ² = cΒ²:

  • 3, 4, 5
  • 5, 12, 13
  • 8, 15, 17
  • Any multiples: 6, 8, 10 (Γ—2 of 3,4,5)

Real-World Application

A ladder 10m long with its foot 6m from the wall:

  • heightΒ² = 10Β² - 6Β² = 100 - 36 = 64
  • height = 8m

3D Pythagoras

Apply the theorem twice to find diagonal distances in 3D shapes.