Pythagorean Theorem Calculator
The Pythagorean theorem calculates relationships in right-angled triangles. It's used in construction, navigation, architecture, and physics to determine unknown lengths. By knowing two sides, you can find the third, essential for designing structures, calculating distances, and solving geometric problems. This fundamental mathematical principle helps in real-world applications like roof construction, road inclination, and space measurements.
Calculator
Enter two known sides:
+Formula
c = √(a² + b²)
How to Use
Enter any two known side lengths of a right-angled triangle in the input fields. Click "Calculate" to get the third side (hypotenuse). Ensure values are positive numbers. Use Clear button to reset. The calculator automatically detects which sides to compute. For best results, measure sides accurately and use same units. Unknown side will be calculated using the relationship c² = a² + b².
Derivation Process
The theorem was developed by Pythagoras, relating three sides of right triangles. Ancient Babylonians used similar concepts. The proof involves arranging four identical right triangles in a square, showing area relationships. Algebraically, expanding (a+b)² reveals c² = a² + b² through area equivalence. Euclid's Elements formalized it geometrically. Modern proofs use algebraic manipulation and geometric similarity principles.
Common Pythagorean Triples
| a | b | c |
|---|---|---|
| 3 | 4 | 5 |
| 5 | 12 | 13 |
| 7 | 24 | 25 |
| 8 | 15 | 17 |
FAQ
1. Can Pythagorean theorem calculate angles?
No, it only calculates side lengths. Use trigonometry (sine/cosine) for angles. The theorem specifically relates the lengths of sides in right-angled triangles but doesn't provide angular measurements.
2. Does it work for all triangles?
Only right-angled triangles. For other triangles, use Law of Cosines. The Pythagorean theorem is specific to triangles containing a 90-degree angle.