Question 1

What is the Pythagorean theorem?

Accepted Answer

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (c) equals the sum of the squares of the other two sides (a and b): a² + b² = c². It was proven by Greek mathematician Pythagoras around 570–495 BCE.

Question 2

What is the hypotenuse?

Accepted Answer

The hypotenuse is the longest side of a right triangle, opposite the 90° angle. It is labeled "c" in the formula a² + b² = c².

Question 3

What are Pythagorean triples?

Accepted Answer

Pythagorean triples are sets of three integers that satisfy a² + b² = c². The most famous is (3, 4, 5). Others include (5, 12, 13), (8, 15, 17), (7, 24, 25), and (20, 21, 29).

Question 4

How do I find a missing leg?

Accepted Answer

To find a missing leg (a), use: a = √(c² − b²). For example, if c=5 and b=4, then a = √(25 − 16) = √9 = 3.

Question 5

Can the Pythagorean theorem be applied in 3D?

Accepted Answer

Yes — the 3D extension is: d = √(a² + b² + c²), used to find the diagonal of a rectangular box.

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About the Pythagorean Theorem

Frequently Asked Questions

What is the Pythagorean theorem?

What is the hypotenuse?

What are Pythagorean triples?

How do I find a missing leg?

Can the Pythagorean theorem be applied in 3D?

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