The Pythagorean theorem

How a² + b² = c² finds a missing side of any right triangle, plus the triples worth remembering.

1 分で読めます2026年10月18日更新執筆：Sumzo teamレビュー：Sumzo team

In a right triangle, the side opposite the right angle is the hypotenuse $c$ — always the longest side. The other two sides are the legs $a$ and $b$ .

a^2 + b^2 = c^2

解き方付き例題

Find the hypotenuse

A right triangle has legs 3 and 4. How long is the hypotenuse?

解き方を表示

Square and add the legs. $c^2 = 3^2 + 4^2 = 25$
Take the square root. $c = \sqrt{25} = 5$

答え： 5

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Finding a leg

Rearrange to $b^2 = c^2 - a^2$ : subtract instead of adding.

解き方付き例題

Find a missing leg

A right triangle has hypotenuse 13 and one leg 5. Find the other leg.

解き方を表示

Subtract the squares. $b^2 = 13^2 - 5^2 = 144$
Take the square root. $b = 12$

答え： 12

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