Applying the Pythagorean Theorem

The Pythagorean Theorem has been known for at least 2,500 years. You use the Pythagorean Theorem when you know the lengths of two sides of a right triangle and you want to figure out the length of the third side.

The Pythagorean Theorem: The sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse:

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Here, a and b are the lengths of the legs and c is the length of the hypotenuse. The legs are the two short sides that touch the right angle, and the hypotenuse (the longest side) is opposite the right angle.

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The preceding figure shows how the Pythagorean Theorem works for a right triangle with legs of 3 and 4 and a hypotenuse of 5.

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