Pythagorean Theorem - How to Use it

Pythagorean Theorem - How it Works - Video

Example 1

Example 1:

To use the Pythagorean Theorem, we must have a right triangle. Once we have established that it is one, then we label the two legs, they form an L shape, and the hypotenuse. The hypotenuse is the longest side and the side that is across from the 90° angle.

Now we can substitute 6 cm or leg A and 8 cm or leg B into the theorem ==> 8² + 6² = c².

Next we follow the order of operations and square both numbers ==> 64 + 36 = c².

Next we add the numbers 100 = c².

Now we have to do an inverse operation to get rid of 2 on c². The inverse of square is square root. So after we take the square root of √c² ==> c then we take the √100 ==> 10 and -10, but we can't have a negative measurement so we cancel the -10.

So our final answer is c = 10 cm or our hypotenuse is 10 cm.

Example 2

Example 2:

To use the Pythagorean Theorem, we must have a right triangle. Once we have established that it is one, then we label the two legs, they form an L shape, and the hypotenuse. The hypotenuse is the longest side and the side that is across from the 90° angle.

Now we can substitute 16 cm or leg A and 12 cm or leg B into the theorem ==> 16² + 12² = c².

Next we follow the order of operations and square both numbers ==> 256 + 144 = c².

Next we add the numbers 400 = c².

Now we have to do an inverse operation to get rid of 2 on c². The inverse of square is square root. So after we take the square root of √c² ==> c then we take the √400 ==> 20 and -20, but we can't have a negative measurement so we cancel the -20.

So our final answer is c = 20 cm or our hypotenuse is 20 cm.

Example 3

Example 3:

To use the Pythagorean Theorem, we must have a right triangle. Once we have established that it is one, then we label the two legs, they form an L shape, and the hypotenuse. The hypotenuse is the longest side and the side that is across from the 90° angle.

Now we can substitute 12 cm or leg A and 13 cm or hypotenuse C into the theorem ==> 12² + b² = 13².

Next we follow the order of operations and square both numbers ==> 144 + b² = 169.

Next we have to do inverse step to get b by itself and subtract the left side by 144 ==> 144 - 144 = 0. So the numbers cancel.

Now we do it to the right side ==> 169 - 144 = 25.

Now we have to do an inverse operation to get rid of 2 on b². The inverse of square is square root. So after we take the square root of √b² ==> b then we take the √25 ==> 5 and -5, but we can't have a negative measurement so we cancel the -5.

So our final answer is b = 5 cm or our leg B is 5 cm.

Live Worksheet 1 - Whole Numbers

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Live Worksheet 2 - Square Roots

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