Learn one of the most important relationships in mathematics, then test your skills with interactive practice problems at every level.
Everything you need to know before solving problems
The Pythagorean Theorem states that in any right triangle (a triangle with one 90-degree angle), the square of the longest side equals the sum of the squares of the other two sides: a² + b² = c²
The hypotenuse is the longest side of a right triangle — the one directly opposite the right angle (90°). It is always labeled c in the formula. The other two sides are the "legs," labeled a and b.
If you know both legs, use c = √(a² + b²). For example, if a = 3 and b = 4, then c = √(9 + 16) = √25 = 5.
Rearrange the formula: a = √(c² − b²). If the hypotenuse is 13 and one leg is 5, then a = √(169 − 25) = √144 = 12.
Test your understanding — try each problem, then check your answer