What is the Pythagorean theorem?

The Pythagorean theorem states that in a right triangle: a² + b² = c², where c is the hypotenuse (longest side). Example: a=3, b=4 → c=√(9+16)=√25=5. This is called a Pythagorean triple (3-4-5). Other common triples: 5-12-13, 8-15-17, 7-24-25.

How do I solve for a leg when the hypotenuse is known?

To find leg b: b = √(c² − a²). Example: hypotenuse c=10, leg a=6: b = √(100−36) = √64 = 8. The same process applies to find leg a: a = √(c² − b²). This is used in navigation, construction, and any right-angle geometry problem.

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