Videos

The Pythagorean Theorem

Added May 01, 2017 •

Copy this URL:
Embed code:	<iframe class="edlio-embed-player" type="text/html" width="640" height="360" src="//talbert.fvsd.us/apps/embed/?v=145729" frameborder="0" allowfullscreen></iframe> Change dimensions

Show Transcript

hey everybody it's me mister I'm and I'm up here at Snow Summit and beautiful Big Bear Lake California  I just riding the slopes little bit carving some snow and you know it made me think I was thinking as I'm riding down the slopes this looks that I'm writing down our kind of like they're kind of like the downhill slanted part of a triangle you know that one side of a right triangle that's like not perpendicular to the other side well that slanted part has a name the name of that slant inside is called a hypotenuse that's a really weird old Greek word hypotenuse hypotenuse happen to be snowboarding down a hypotenuse right now here take a look I like hypotenuse this I thought misses are cool tried all kinds of fun for skiers and snowboarders leather covered with snow I highly recommend that you enjoy yourself I bought you some time to you know what speaking of hypotenuse isn't right triangles what do you want to share a little bit more info with you put Sagarin theorem yes indeed we've talked about Pythagoras now turn the talk about the Pythagorean theorem which is named after him yesterday we said the Pythagoras noticed a strange relationship between the three sides right triangle remember there's two legs and a hypotenuse well what Pythagoras and all is Pythagorean buddies noticed is it all right triangles have side obey this formula the square of one leg plus the square of another leg equals the square of the length the hypotenuse so we saw that with the 3 4 5 right triangle  but it works with any right triangle so if add one leg is 9 ft another leg is 12 ft then the hypotenuse would have to be 15 ft that's the only way that this trying good work and I'll show you why  one leg squared  would be 81 another legs squared wood play 12 squared and that's 144 when you add those two together 81 + 144 you get 225 and that number has to be the hypotenuse squared so  that never happens to be mean squared so the hypotenuse must be 15 and it works for every single right triangle in the it's true there has never been a right triangle that does not obey that formula and so it's a pretty famous formula in math and it's called the Pythagorean theorem and it is that the square of one leg plus the square of another like equals the square of the hypotenuse or we'd like to abbreviate that because instead of saying leg squared plus leg squared equals hypotenuse squared it's a lot easier to just say a squared plus b squared equals c squared the equation that most people mean when they say the Pythagorean theorem the Pythagorean theorem is really an equation and the equation is a squared plus b squared equals c squared where A and B are the two legs of a right triangle and C is the hypotenuse of a right triangle by the way this only works for what kind of triangle a right triangle all right so I'm just going to abbreviate that up here we're going to use a squared plus b squared equals c squared yeah so you know what it's interesting because if you want to find the length of the hypotenuse of a right triangle all you have to do is know the length of the two legs because each of the two legs will call them A and B can be squared and then added together and that will equal the square of the length of the hypotenuse this is what we called Zachary in theorem AKA a squared plus b squared equals the hypotenuse or c squared that's the Pythagorean theorem and that's pretty cool thing we're going to use that to solve the problem the problem is I don't know the third side of this triangle you know that one leg is 8 and I know then another leg is 6 but what is the hypotenuse we don't know the measurement of that hypotenuse but we can use the Pythagorean alarm to find it so let's do that  one of the legs squared would be that 6 squared the other leg squared would be 8 squared  the hypotenuse is X we don't know what it is so we have to just call it X and when we put the Plus in the equals in there we get sick where to plus a squared equals x squared and now we're just going to use algebra to solve this equation what's 6 squared 36 what's 8 squared 64 can you add 36 and 64 together sure that makes a hundred  wait a second a hundred equals x square what number squared makes must be 10 because 10 is the only number that when you square gives you a hundred and does it look like in this case acts could be about 10 if the others are six and eight that's seems like that makes sense remember that I bought is always the longest of the three sides  but what if it wasn't a nice number like a hundred what if this head tell us an equation where it was like x squared equals 103 and you can't really unsquare 103 and very nicely what would you do in a like that well sometimes Pythagorean theorem problems come out nice and sometimes they don't come out so nice so here's one that's not going to come out quite so Knights also on this problem noticed the missing piece isn't the hypotenuse  which one is the hypotenuse  the hypotenuse the five isn't it so the axe is one of the legs the other leg is too and the hypotenuse is 5 so x squared + 2 squared equals 5 squared is how we're going to fill in our a squared plus b squared equals c squared Pythagorean theorem now I can simplify this I don't know what it is but I know what two squared is and I know what 5 squared is 2 * 2 is 45 * 5 is 5  how am I going to get backs oh yeah I've got to subtract 4 from both sides so I can get x squared by itself hopefully I didn't lose you by subtracting for from the 25 but then what number squared makes 21 I don't know how to Square 21 oh wait a second if I want to unsquare the axe to figure out what x equals I've got to unsquare the 21 as well the math word for on squaring is square rooting so at this point you kind of have to use your calculator because I don't think any of have the √ 21 memorized in fact that's an irrational number it's one of those yucky decimals it's going to keep on going on and on forever but when you round it it comes out to approximately 4.58 or we could say that X is about 4.6 in this case alright that was an example of a more Ricky Pythagorean theorem problem so I gave you an easy one and I gave you a more challenging one and now it's your turn  here's an ZR1 and a simpler one and the answer to this one should come out to a nice rational number here's a weird one and you're not solving for the hypotenuse this time you're solving for one of the legs your answer is not going to come out nice and rational it's going to be one of those yucky decimals and you're going to have to square root something on your calculator and have it yeah messy long number that you're going to have to round at the end  alright if you can handle those two problems you are make the Tiger in theorem machine and that is all we have to say today

Uploaded by Jeff Marbut.

Videos

The Pythagorean Theorem

More videos from Jeff Marbut