Pythagoras
A standard method from Geometry and data basics: the steps and worked examples.
Steps
- Find the hypotenuse (the side opposite the right angle).
- Hypotenuse² = sum of the squares of the other two sides.
- Converse: if c² = a² + b², the angle opposite c is 90°.
Worked examples
Example 1: Pythagoras' converse: a triangle has sides 5, 12 and 13. Is it right-angled?
5² + 12² = 25 + 144 = 169 = 13². Yes; by the converse of Pythagoras' theorem, the angle opposite the side 13 is 90°.
Example 2: Pythagoras: a 5 m ladder leans against a wall with its foot 1.4 m from the wall. How high up the wall does it reach?
the ladder is the hypotenuse (opposite the right angle at the wall's foot)
h² + 1.4² = 5²
h² = 25 − 1.96 = 23.04
h = 4.8 mFor the whole topic, read Geometry and data basics: key points, common mistakes and how the DSE tests it.