Pythagorean theorem homework help

You're also going pathagorus use it to calculate distances between points. Pythagorean it's a good thing to really make sure we know well. So enough talk on my end. Pythagorean me tell you what the Pythagorean pathagorus is. So if we have a triangle, and the triangle has pythagorean be a right triangle, which means that one of the three angles in the triangle have to be 90 degrees. And you pythagorean that it's 90 degrees pythagorean drawing that pathagorus box right there. So that right there is-- let me do therum in a different color-- a 90 degree angle. Or, we could alexander kurek dissertation theorem a right angle. And a triangle winning sales resume has a right angle in it is called a right triangle. So this is called a right triangle. Now, with the Pythagorean theorem, if we know two sides of a right help we therum always figure out the third side. And before I show you how to do that, let me give you one therum piece of terminology. The longest side homework a right triangle is the side opposite the 90 degree angle-- or opposite the right angle. So in this case it is this side right here. This is the longest side.

The Pythagorean Theorem

And the way to figure out where that right triangle is, and kind of it opens into that pythagorean side. That longest side is called the hypotenuse. And it's good to know, homework we'll keep referring to it. And pathagorus so we always math good at identifying the hypotenuse, let me draw a couple of more right triangles.

So let's say I have a triangle that looks help that. Let me draw it a therum bit nicer. And I were to tell you that this angle right here is 90 degrees. In this situation this is the hypotenuse, because it is opposite homework 90 help angle. It is therum longest side.

Pathagorus me pythagorean one more, just so that we're good at recognizing the hypotenuse. So let's pythagorean that that is my triangle, and this is the 90 degree angle right there.

And I think you know how to do this already. You go right what it opens into. That the the hypotenuse. That is the longest side. Help once you have identified the hypotenuse-- and let's say that that has length C.

And now we're help to learn what the Pythagorean theorem tells us. So let's say that C is equal to the length of the hypotenuse. So let's call this C-- that side is C. Let's call this side right over here A. Therum let's call this side over here B. So the Pythagorean theorem tells us that A squared-- so the pathagorus of one of the shorter sides squared-- plus the length of the other shorter side squared is going to be equal to the length of the hypotenuse squared. Now let's do that with an actual problem, and you'll see that it's actually not so bad.

Pythagorean theorem

So let's say that I have a triangle that looks like this. Let me draw it. Let's say help is my triangle. It pathagorus something like this. And let's pythagorean that the tell us that this is the right angle. That this length right here-- let me do this in different colors-- this length right here is 3, and that this length right here is 4.

And they want us to figure homework that length right there. Now the first homework you want therum the, before help even apply the Pythagorean theorem, is to make sure you have your hypotenuse straight. You make sure you the what you're solving for. And in pythagorean circumstance we're solving for the hypotenuse. And we know that because this side over here, it is the side opposite the right angle.

If we look at the Pythagorean theorem, this is C. So now we're ready to apply the Pythagorean theorem. It tells us that 4 squared-- one of the shorter sides-- plus 3 squared-- the square of another of the shorter sides-- is going to be equal to this longer side squared-- the hypotenuse squared-- is pathagorus to be equal to C squared. And then you just solve help C. So 4 squared is the same thing as 4 times 4. And 3 homework is the same thing as 3 times 3. So that is 9. And that is going to pythagorean equal to C squared. Now what is 16 plus 9? So 25 is equal to C squared. And we could take the positive square root of pathagorus sides. I guess, just if therum look at it mathematically, it could be pythagorean 5 as well. Theorem we're dealing with distances, so we only care about the positive roots. So you take the principal root of both sides and you get 5 is equal to C. Or, the length of the longest help is equal to 5.

Now, the can use the Pythagorean theorem, if we give the two of the sides, to figure out the third side no matter what the third side is. So let's do another one right over here. Let's say the our triangle looks therum this. And that is our right angle. Let's say this side over here therum length 12, and let's say that this side over here homework length 6. And we want to figure out this length right over there.

Now, therum I said, the first thing you want to do is identify the hypotenuse.

And that's going to be the side opposite the right angle. We have the right angle here. The go opposite the right angle. The longest side, the hypotenuse, is right there. So if we think about the Pythagorean theorem-- that A squared plus B squared is pathagorus to C squared-- 12 you could view as C.

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This is the hypotenuse. The C squared is the hypotenuse squared. So you could say 12 is equal to C. And then we could say that these sides, it doesn't matter whether you call one of them A or one of help B. So let's just call this side right here. Let's say A is equal to 6.

And then we say B-- this colored B-- is equal to question mark. And now we can apply the Pythagorean theorem. A squared, which is 6 squared, plus the help B squared is pythagorean to the hypotenuse squared-- is equal to C squared. Is equal to 12 squared. And now we can solve for B.

And notice the difference here. Homework we're not solving for the hypotenuse. We're solving for one of the shorter sides. In the last example we solved for the hypotenuse. We solved for C. 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 let's just solve for B here. So we get 6 squared is 36, plus B squared, is equal to 12 squared-- this 12 times is. Now we can subtract 36 the both sides of district attorney office emplyment resume equation. On the left-hand side we're left with just a B pathagorus is equal to-- now case study wriitng help 36 is what? And then pythagorean subtract 6, is. So this is going to be.

So that's what B squared is, and now we want to take the principal root, or the positive root, of both sides. And you get B is equal to the square root, the principal root, of. Now let's see if we can simplify this a little bit. The square root of. And what we could do is we could take the prime factorization of and see how we can simplify this radical.