Pythagorean Theorem

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The Pythagorean Theorem is a handy way to find the side lengths of a right triangle. A right triangle has one right (90°) angle. According to the theorem, the sum of the squares of the two sides that make up the right angle is equal to the square of the third side. This third side, the one across from the right angle, is called the hypotenuse.


As a formula, the Pythagorean theorem looks like this: a² + b² = c², where a and b are the sides next to the right angle, and c is the side across from it. 


Let's look at an example. If a right triangle has a length of 3 inches and a height of 4 inches, what would be the length of the hypotenuse? Just substitute the given values and solve:

  • a² + b² = c²
  • (3 in)² + (4 in)² = c² [We put the side lengths in parentheses to show that the number and the unit (inches) need to be squared. Without the parentheses, you might be confused and think that we mean "three square inches."]
  • 9 in² + 16 in² = c² 
  • 25 in² = c² 
  • 25 in² = √c² [To solve, find the square root of each side. Of course, the square root of c² will just be c. You can use the √ function on your calculator.] 
  • 5 in = [In other words, the length of the hypotenuse is 5 inches. Nice job!]