 Welcome back today what we're going to do in this video is talk about the 45 45 90 special right triangles Okay, what I'm going to do in this video is I'm just going to talk about just a just two examples of Solving for either the hypotenuse or one of the legs of a 45 45 90 triangle Okay, with these right triangles There's a special pattern that kind of happens and here in the bottom right corner kind of provided a picture I've kind of in general what they do so for a 45 45 90 triangle the legs are going to be the same so technically this is also a Isosceles triangle a little extra fact there to get from the leg to the hypotenuse of this 45 45 90 triangle What you have to do is simply just multiply by the square root of 2 Okay, and then to get back if you know what the hypotenuse is to get back to one of the sides All you have to do is divide by the square root to okay So it's actually a pretty simple straightforward process to find all these different sides of a 45 45 90 triangle Again, we call these special right triangles because they there's a certain pattern that happens with them Okay, so for this example what you have to do with these special right triangles is first of all You got to have to identify what kind of triangle it is Well, obviously it's a 45 this angle up here would be 45 90 triangle Okay, and then what you have to do is identify what you're looking for in this case We are looking for the hypotenuse of one of these sides So what I have to do is I have to go from the leg to the hypotenuse Okay, of this right triangle So if I look at my little diagram here if I go from a leg to the hypotenuse all I have to do is just multiply by the square root of 2 Okay, so in this case this this one's actually pretty easy to find x in this case is going to be equal to 8 root 2 Okay, I take 8 and take it times a square root of 2 to get to the hypotenuse now 8 times a square root of 2 if I can grab a handy dandy calculator real quick 8 times the square root of 2 is going to be about Okay, and a little bit decimal here about 11.3137 There's more decimals after that that kind of thing Okay, but what that does tell us is that the hypotenuse is always supposed to be the longest side of a right triangle and in this Fetting in this case 11.3 is bigger than 8 so we know we did that correctly all right Also the directions here find the value of x give your answer in simplest radical form That's why I circled this one is because 8 times a square root of 2 that is simplest radical form this right here This decimal is definitely not radical form. So we would not include that in our answer Okay, so that's a pretty simple First example the second example okay same directions find the value of x give your answer in simplest radical form So here is our second triangle our second example here in this case We're going we we know what the hypotenuse is hypotenuse right here and we're going backwards to one of the legs Okay, I've provided the picture down here again if I go from the hypotenuse of this triangle back to one of the legs I have to divide by the square root of 2 Now this one's gonna be a little bit tougher because you're dividing by a radical so in this case What I have to do is I have to take five if I'm going from the hypotenuse back to one of the legs I have to take five and I have to divide by the square root of 2 To get back to where I originally was now That is really confusing that right there is a number divided by the square root of 2 Well, we don't even know what the square root of 2 is we're dividing by an infinitely repeating decimal It's also known what also we can call it an irrational number. It just doesn't make a whole lot of sense So what we have to do in this situation is if we want to give our answer in simplest radical form This is not the simplest. Okay, this radical on the bottom is very very messy So what we have to do in this case is What we're going to do to get rid of this radical on the bottom to get rid of that square root of 2 on the bottom What we're actually going to do is we're going to multiply by the square root of 2 on top and on bottom okay Now this is what we call this is also another math phrase that we have it's called Rationalizing the denominator. Okay, so what we do here is we're trying to make the bottom part here a rational number That's why it's called rationalize the denominator, but anyway So to get rid of the square root of 2 multiply both the top and bottom by the square root of 2 these top and bottom They actually don't multiply so I'm just going to stick them next to each other Five is on the outside two's on the inside. They don't multiply times one another So just put them right next to each other on the other hand on the bottom here These numbers are actually going to multiply. Okay, since they're both inside the radical they do multiply together So you get the square root of 4? Okay, now we can do one more step of simplifying. We actually know what the square root of 4 is the square root of 4 is in fact 2 Okay, so now and again back to that phrase Rationalizing the denominator the denominator has gone from an irrational number of the square root of 2 now It is a rational number of 2 it's a much nicer Easier number dividing by 2 is much easier than dividing by the square root of 2 Anyway, what this means is that my leg is equal to 5 root 2 over 2 You could also write it as 5 halves root 2. I've also seen it written that way either way That is our answer. That is the leg of the right triangle. Okay, so there's just a couple of examples to help you with Help you with your 45 45 90 special right triangles. Alrighty and hopefully this video was helpful for you today Thank you for watching and we'll see you next time