Pythagorean Theorem
Relates the three sides of a right-angled triangle.
a^2 + b^2 = c^2
1What it means
In a right-angled triangle, the square of the longest side (the hypotenuse, c) equals the sum of the squares of the other two sides.
2Variables
| Symbol | Meaning |
|---|---|
| a | One leg (shorter side) |
| b | Other leg |
| c | Hypotenuse (side opposite the right angle) |
3Worked examples
Example 1 Worked solution
Q. A ladder’s foot is 3 m from a wall and its top reaches 4 m high. Find the ladder length.
- The ladder is the hypotenuse c.
- c² = 3² + 4² = 9 + 16 = 25.
- c = √25.
✓ c = 5 m
4Where it's used
- ✦Finding distances and diagonals you cannot measure directly.
- ✦Checking if a corner is a perfect right angle (3-4-5 rule).
5Tips & common mistakes
- !The hypotenuse is always opposite the right angle and is the longest side.
- !Remember common triples: 3-4-5, 5-12-13, 8-15-17.