Frequently Asked Questions
What is the Pythagorean theorem?
In a right triangle: a² + b² = c², where c is the hypotenuse (longest side, opposite the 90° angle). Only applies to right triangles.
How do I find the hypotenuse?
c = √(a² + b²). Example: a=3, b=4 → c = √(9+16) = √25 = 5.
How do I find a missing leg?
If you know c and a: b = √(c² - a²). Example: c=13, a=5 → b = √(169-25) = √144 = 12.
Does it work for all triangles?
No, only right triangles. For others, use the Law of Cosines: c² = a² + b² - 2ab·cos(C).
What are common Pythagorean triples?
Integer triples: (3,4,5), (5,12,13), (8,15,17), (7,24,25), (6,8,10), (9,12,15), (20,21,29). Multiples also work.
Who discovered the Pythagorean theorem?
Named after Pythagoras (c. 570–495 BC), but known to Babylonians (~1900 BC) and Indians (~800 BC) earlier.
How is it used in real life?
Construction (square corners), navigation (shortest path), architecture, computer graphics, physics (vectors).
What is the converse?
If a² + b² = c² for a triangle, then it's a right triangle with the right angle opposite side c.