Pythagorean Theorem — a² + b² = c²
Variable Key
a= leg (short side)b= leg (other short side)c= hypotenuse (longest side, opposite 90°)
Find hypotenuse c
Given both legs a and b.
Find leg a or b
Given the hypotenuse and one leg.
Find a
Find b
Pythagorean triples
Integer right triangles (whole number sides).
3-4-5
5-12-13
8-15-17
a= leg (short side)
b= leg (other short side)
c= hypotenuse (longest side, opposite 90°)
The Pythagorean theorem states that in any right triangle, the square of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the other two sides. Written as a² + b² = c², where c is the hypotenuse.
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Tip: When two sides have a ratio close to 3:4, check if the third side is 5× the GCD. This instantly confirms a 3-4-5 family triple.
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Fun Fact
There are over 370 known proofs of the Pythagorean theorem — more than any other theorem in mathematics. One was written by US President James Garfield in 1876.
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