The Pythagorean Theorem Assignment Answers Topic On Research Paper
It's useful in geometry, it's kind of the backbone of trigonometry. So we have the square root of 108 is the same thing as the square root of 2 times 2 times-- well actually, I'm not done. So this is the same thing as the square root of 2 times 2 times 3 times 3 times the square root of that last 3 right over there. And, you know, you wouldn't have to do all of this on paper.
You're also going to use it to calculate distances between points. So if we have a triangle, and the triangle has to be a right triangle, which means that one of the three angles in the triangle have to be 90 degrees.
If you're seeing this message, it means we're having trouble loading external resources on our website. So that's what B squared is, and now we want to take the principal root, or the positive root, of both sides. So the length of B, you could write it as the square root of 108, or you could say it's equal to 6 times the square root of 3. And the square root of 3, well this is going to be a 1 point something something.
If you're behind a web filter, please make sure that the domains *.and *.are unblocked. So that's why it's always important to recognize that A squared plus B squared plus C squared, C is the length of the hypotenuse. So we get 6 squared is 36, plus B squared, is equal to 12 squared-- this 12 times 12-- is 144. And you get B is equal to the square root, the principal root, of 108. So this is the square root of 36 times the square root of 3. So it's going to be a little bit larger than 6.
So it's a good thing to really make sure we know well. And you specify that it's 90 degrees by drawing that little box right there.
So that right there is-- let me do this in a different color-- a 90 degree angle. And a triangle that has a right angle in it is called a right triangle. Now, with the Pythagorean theorem, if we know two sides of a right triangle we can always figure out the third side. And then we say B-- this colored B-- is equal to question mark. A squared, which is 6 squared, plus the unknown B squared is equal to the hypotenuse squared-- is equal to C squared.
And in this circumstance we're solving for the hypotenuse. So now we're ready to apply the Pythagorean theorem.
In this situation this is the hypotenuse, because it is opposite the 90 degree angle. Let me do one more, just so that we're good at recognizing the hypotenuse. So let's say that C is equal to the length of the hypotenuse. So let's say that I have a triangle that looks like this. And they want us to figure out that length right there. And that's going to be the side opposite the right angle.
So let's say that that is my triangle, and this is the 90 degree angle right there. Now the first thing you want to do, before you even apply the Pythagorean theorem, is to make sure you have your hypotenuse straight.
In this video we're going to get introduced to the Pythagorean theorem, which is fun on its own. Now we can subtract 36 from both sides of this equation. On the left-hand side we're left with just a B squared is equal to-- now 144 minus 36 is what? Now let's see if we can simplify this a little bit. And what we could do is we could take the prime factorization of 108 and see how we can simplify this radical.
But you'll see as you learn more and more mathematics it's one of those cornerstone theorems of really all of math. So 108 is the same thing as 2 times 54, which is the same thing as 2 times 27, which is the same thing as 3 times 9. And so, we have a couple of perfect squares in here. And this is all an exercise in simplifying radicals that you will bump into a lot while doing the Pythagorean theorem, so it doesn't hurt to do it right here.