Pythagorean Theorem: Finding the Length of the Hypotenuse | Math with Mr. J

welcome to math with Mr Jay [Music] this video I'm going to cover how to find the length of the hypotenuse using the Pythagorean theorem now remember we use a squared plus b squared equals c squared with C always being the hypotenuse and then A and B being the legs if we know the lengths of two sides of a right triangle we can use the Pythagorean theorem to find the length of the third side let's jump into our examples starting with number one where we have a right triangle and we are given the lengths of the legs the hypotenuse is unknown remember the hypotenuse is the longest side of a right triangle and the side across from or opposite of the right angle so let's use a squared Plus B squared equals c squared in order to find the length of the hypotenuse now again C is always the hypotenuse so this is C and then the legs are A and B let's make this a and this B now keep in mind it does not matter which leg is a and which leg is B now we can plug in the side lengths that we are given and work through the equation in order to find the length of the hypotenuse so a is eight meters so let's plug in 8 for a so 8 squared plus b is 6 meters so plug in 6 for B so 6 squared equals c squared 8 squared gives us 64. plus 6 squared gives us 36. 64 plus 36 is 100 so 100 equals c squared our next step is to isolate C in order to figure out what C equals so again we are just working through this equation to figure out C since C is being squared let's take the square root in order to isolate C whatever we do to one side of the equation we must do to the other so we need the square root of 100 as well c is now isolated so we have C equals and then the square root of 100 is 10. so C equals 10. let's rewrite that with C coming first so C equals 10 and this is meters so the hypotenuse measures 10 meters and that's our missing side length let's move on to number two where we have a right triangle and again we need to find the length of the hypotenuse we are given the two legs we have 10 feet and seven feet so let's use a squared plus b squared equals c squared in order to find the hypotenuse let's call this leg a this leg B and then the hypotenuse is C now we can plug in and work through this equation so for a we have 10 feet plug in 10 for a so 10 squared plus 7 feet for B so plug in 7 for B 7 squared equals c squared 10 squared that's 100 plus 7 squared that's 49. equals c squared 100 plus 49 that gives us 149 equals c squared now we have 149 equals c squared so our next step as we work through this equation is to isolate c c is being squared so let's take the square root in order to isolate C whatever we do to one side of the equation we must due to the other so let's take the square root of 149 as well we end up with an isolated C on the right side of the equation and then as far as the square root of 149 149 is not a perfect square so we do not end up with a whole number answer C equals the square root of 149. now we can write the square root of 149 as an approximate rounded decimal the square root of 149 is irrational the decimal never stops and it doesn't repeat so again let's round it and we will round it to the hundredths place so the square root of 149 gives us 12 point two zero six and again that just continues on so I'm going to write it to the thousandth place and then round it to the hundredths so let's round it to the hundredths place we have a 6 to the right in the thousandths so this rounds up so the square root of 149 is approximately 12 and 21 hundredths so C is approximately 12 and 21 hundredths and this is feet so the hypotenuse is approximately 12. and 21 hundredths again this is feet so there you have it there's how to find the length of the hypotenuse using the Pythagorean theorem I hope that helped thanks so much for watching until next time peace