Pythagoras’ theorem · Year 11
In Year 11 you learn: Pythagoras in 3D.
In a right-angled triangle, the square on the longest side (the hypotenuse, opposite the right angle) equals the sum of the squares on the other two sides. Pythagoras’ theorem finds a missing side, a distance between points, or checks whether a triangle has a right angle.
Key facts
- a² + b² = c², where c is the hypotenuse.
- Finding the hypotenuse: add the squares, then square root.
- Finding a shorter side: subtract the squares (c² − a²), then square root.
- Distance between two points: √((change in x)² + (change in y)²).
- In 3D, the longest diagonal of a cuboid is √(l² + w² + h²).
- If a² + b² = c² for the sides, the triangle is right-angled.
Worked examples
Example 1
A 6 m ladder leans against a wall with its foot 1.5 m from the wall. How high up the wall does it reach, to 1 d.p.?
Answer: 5.8 m