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>> Hi guys, my name's Lindsay and today we're going to take a look at Pythagorean theorem.
Now I've got it written up here above my head and as you can see,
I've got H squared equals A squared plus B squared.
You may have seen it written in different ways, maybe using an A,
a B, and a C. The reason I like to write it this way is because the H stands for hypotenuse.
And the hypotenuse is, if you see here, I've written use only for right triangles?
The Pythagorean theorem only works when you've got a triangle with a right angle in it.
That little square implies a right angle, which hopefully you know means a 90-degree angle.
This doesn't work if you don't have a 90-degree angle in your triangle.
But this example that I do, that I have here, does.
So, let's try it. We've got the hypotenuse, which if you take a look at the right angle,
the side directly across from it is the hypotenuse. Not the other two sides, this guy.
So, when we're looking back at the formula, the important thing to remember is that the H
is on one side by itself and the other two sides, we can call them A and B,
and it doesn't matter if this side is A and that is B,
or vice versa, they're kind of interchangeable, but the hypotenuse is important.
It's got to be sitting by itself.
So, let's say, for example, in this triangle, if our A side is 3, let's do millimeters
and our B side is 4 millimeters.
And the question would be then, what is the hypotenuse?
So, we can use Pythagorean theorem to do that. So let me rewrite it here.
So, we know that H squared equals A squared plus B squared. And I'm going to plug my values in for A,
3, and my value for B in as well, which is 4.
So, let's rewrite that. So, H squared equals 3 squared plus 4 squared.
Now if you want to, you can go ahead and square those numbers in your head or in your calculator.
But something else that we need to talk about is that we've got a squared in front of our H.
I don't want to know what the hypotenuse squared is, I want to know what the hypotenuse is.
So, the way that we're going to deal with that is we are going to take the square root of this
H squared, and if you do something to one side of an equation,
you've got to do the same to the other. So, I'm going to take the square root of this.
And the reason we did that is because the square root and the squared cancel each other out.
So, I'm left with just an H, just the hypotenuse by itself.
Square root sign stays on the right-hand side.
Let's square these, 3 squared which is 9. 4 squared, which is 16. And then make sure
in your calculator or however you're calculating this, a square root sign's kind of like a bracket.
I actually have to add those numbers together before
I press that square root button on my calculator if that's the way I'm calculating this.
So, 9 plus 16, that's 25.
And once I've added those together, I can take the square root of 25, which you probably know is 5.
And if these two were in millimeters, these lists would be in millimeters as well.
So, let's put that there. So again, a couple things to think about here.
Make sure that your hypotenuse is on one side by itself
and make sure that you're following your order of operations, you're doing this calculation
under the square root sign before you are pressing that square root button on your calculator.
So, let's try a second one. Let me grab a different colour here.
This only works for right triangles.
So, let's draw you a second right triangle.
This guy's upside down, but that doesn't matter, it's still a right triangle.
And I'm going to give you two sides.
So, let's give you numbers that may be a little bit more difficult than list.
Let's say this is 12.5 kilometers and this guy is 6 kilometers.
So, my question here would be find the hypotenuse.
So why don't you take a minute and use Pythagorean theorem
the same way we did over here to find the hypotenuse on this question,
I'm going to make myself some room and then we'll come back and check it together.
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Alright guys, I'm back. And this time we're going to try this guy.
Now the numbers are a little bit more difficult to work with maybe.
We've got a decimal, but that's okay. We're just going to deal with this the same way.
But the key to this question is going to be that these two guys are our A and B value
and the hypotenuse is staying on the other side by itself.
So, something to think about is if I wanted to,
I could actually rewrite this Pythagorean theorem as H, or sorry, H equals the square root of
12.5 squared plus 6 squared.
So, I've sort of skipped that step of eliminating the squared by putting the square root.
They actually both mean the same thing.
So, if you want to skip that step, that's fine.
So now I'm going to grab my calculator and figure these out.
And I'm going to make sure that first I figure them out separately, so 12.5 squared
is... 156.25…and 6 squared is 36.
And I am going to make sure that I add those two together first.
You might, when you're, if you're looking at the question, hopefully you completed on your own,
maybe you skipped right to the answer. That's fine.
I'm just going to make sure that I am showing that it's important to make sure that we
do this one step at a time.
So, I've got 192.25. And that is what I'm going to find the square root of.
So, depending on your calculator,
I can just hit the square root button now with 192.25 on my screen.
You might have to clear it and write,
type the square root button first depending on the calculator.
But for me, I can just press that square root button, so I'm going to do that.
And I get 13., if I'm rounding to one decimal place, 13.9.
And... If these are both in kilometer’s, so is this.
So, there's the distance of my hypotenuse.
And also, one last thing to keep in mind, since this 90-degree angle is the biggest
of these three angles in the triangle, the side directly across from it is also the biggest side.
So, 13.9, well that's bigger than 12.5 and it's bigger than 6, so that's just kind of
a nice way to check to make sure that you are correct or you're on the right track.
So hopefully that helps. In this video, we're just focusing on finding the hypotenuse.
If you want to take a look at finding one of the other two sides,
take a look at one of our other videos.
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