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45-45-90 Right Triangle Practice

In mathematics, the number 45 (forty-five) is a natural number that follows 44 and precedes 46.

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Video Transcript

our guests are back with some practice on 45. 45 90. Right triangles Recall that the relationship between the sides of a 45 45 90 right triangle would be that obviously the two legs of the same length in the high partners is always gonna be radical. Two times that length. A couple of things. Obviously you have a nice sausages triangle. You're gonna have to equal opposite sides or angles. Pardon me? That's why they're both 45. 45. And the way that I approached it is that technically, this is part of a square. And so if you were to draw that diagonal down the you know through a square, it's gonna cut those 90 degree angles at 45. 45. So two ways to look at that. And so let's talk about some of these problems here now. All right, let's look at question one. If we know that this side length is five, pardon me. Then, by default, we know why he's gonna be five and using our little rule here. We know this is gonna be five or to the iPod news. Likewise. Down a question three. We know one of the legs is seven. That means the other leg is seven. And again, the high part news is gonna be seven Ruutu That straightforward. Okay, now, if you're given a question where your leg has a route to already in it, that's OK. The other leg is going to be eight route to, but the high pot news is supposed to be route two times the given leg. So we're going to say that this is eight route to times route to where this is the leg length times that route to which we found by doing in the previous video. So this is gonna be eight times to remember that a radical type of self cancels the radical out and you could be left with 16 perhaps. You know that. Okay, on question six, this is another one of those straightforward ones. Here we have the iPod news. The hypotenuse is the ex route to side. So the fact that it's got a route to on it, I could just basically say B and air both equal to nine units. Likewise down and eight high partners has the radical to side. I could just say that both X. And why are 15 since you would multiply those legs by radical, too, to get their partners? Okay, so here's an example. Let's say yeah of a problem where the high partners is just too. Its's a nice integer. And we saw this with the 30 60 90 right triangles where we're used to seeing a route to on here. Well, there is no route to on there. That's because whatever X was when we multiplied it to get to the high pot news by route to something must have canceled to get just a ninja value. Otherwise we'd have a rational or sorry radical hanging out. Remember, the high partners in this case to is the X radical to site. So if I divide by route to I get to of a route to equals X and if you recall, I have to rationalize this. You don't have to, but it's common practice to do so that ends up being radical. Two squared. Remember the radicals cancel. She loved to. So you're left with two route to over two equals X and, in other words, these cancel. And so you're left with X Equalling route to which then by default beans. Why also equals route to So it could be that you have to do a little bit of rationalizing. But I can also show you a shortcut here in just a second. Let's go ahead and take a look at, um 14, for example. Again, we're used to this being the route to side. So whatever you or via Z 20 must have been you times route to. Well, for that to be the case, that means 20 must have been I'm sorry. That must mean you must have been equal to 20 over route to, which is a fine answer. Both of these were equal to 20 route to however, most mathematicians or textbooks or whatever, don't like radicals in the bottom. So we'll go ahead and rationalize it by multiplying by the radical that's in the bottom of the fraction. Remember, radical times itself cancels, so we're left with 20 route to over two, which equals 10 route to So The shortcut for this, by the way, is if this number and the iPod news doesn't have a radical attached to it, a radical too attached to it, you could just divide it by two and then slap a radical to on it. Otherwise, the technical procedure will be to take whatever the high pot news is set equal to the leg. Times radical to solve for the leg rationalized if you have to. So I saw a really good example of one right here. So here, that here's the iPod news. It's nine nine. Should be, you know, route two times this leg or this leg. You could have said a white equals were too for why we're too That means nine over route to equals X. I'm fine with you saying that this is nine over Ruutu and therefore this is nine over Ruutu. There's nothing wrong with that again. Lots of textbooks and mathematicians. They're gonna want you toe rationalize it. So that's easier toe, I guess. Do some mental math. But it these were going to cancel in terms of the radicals you just get to so you get nine or two over to I mean, I guess you could say 4.5 or two, but nine or 2/2 is just fine For why? Which means exit Also equal nine through two over to so these air several examples of how you would just solve a triangle. So imagine any kind of word problem where you have any kind of 45. 45 Mandy, right? Triangle or 36 90 right triangle, for that matter. Um, in relation to the previous movie or movies about that special right triangle, you could go ahead and apply. So it is very important to know these two special right triangles, the ratios that exist between the side length, um, for your everyday knowledge, but also for your standardized standardized test practice. Um, And for your problem solving. So anything that involves a square somewhere lurking in there is a 45 45 90. Anything that involves especially unequal lateral triangle, um is there's really lurking at 30 60 90 triangle. There. Okay, I will see you next time.