What Is Pythagorean Theorem?
The Pythagorean Theorem states that in a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.
Examples of Pythagorean Theorem
1
3² + 4² = 5²2
5² + 12² = 13²3
8² + 15² = 17²Formula and Key Points
Formula / rule
a² + b² = c²
- It applies only to right-angled triangles.
- The hypotenuse c is opposite the right angle.
- It can be used to find a missing side length.
- The converse can help test whether a triangle is right-angled.
Why This Matters in Computer Science
Used in graphics, games, robotics, computer vision, spatial algorithms and coordinate calculations.
Worked Example
Problem
A right triangle has legs 6 and 8. Find the hypotenuse.
- Use a² + b² = c².
- Substitute: 6² + 8² = c².
- Calculate: 36 + 64 = 100.
- Take the square root: c = 10.
✓
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Final Answer10
Triangle Side Roles
| Side | Meaning | Example value |
|---|---|---|
| a | One leg | 6 |
| b | Other leg | 8 |
| c | Hypotenuse, opposite 90° | 10 |
Related Math Terms
Pythagorean Theorem: Frequently Asked Questions
When can I use the Pythagorean Theorem?
Use it for right-angled triangles when you know two side lengths and need the third.
Which side is c?
c is the hypotenuse, the longest side opposite the right angle.