All right, and Welcome to Introduction to trigonometry. And in this section here, we're going to talk about angles. angles in a right triangle, what a right triangle is solving z with a right triangle. And we'll define what z is when we get there. And trigonometry triangle properties and how we use them. Alright, so let's stop and go to the next section.

Okay, what is an angle, an angle is formed when two lines meet. And if you can see here, I give you an example. So we this is a line we have a line here and a line there. This one is, is going counterclockwise, so This is zero was saying, Okay, we've got the angle, the angle is 30 degrees to the left. This one here. They meet here.

This one here is 660 degrees, or 60 separate divisions which we call degrees. This one is 90. All right. Now, the point I'm trying to make is, we call it degrees, I'm going to say a degree is a equal segment. So if I take a circle and I break that up into 360, equal segments which we call degrees, we're saying there are three Hundred and 60 degrees in a circle. So if I start here and go all the way around here, that's 360 what I'm showing you right there.

All right. So we have specific, not specific, but you'll hear specific. When somebody says, okay, it's 180, it's 90. Well, when I'm at 90 degrees, that's really a right angle. All right, because I've got zero here and 90 here. And basically, that's what I'm showing you there.

All right. And then as I come around another 90, that's 180. Okay, but you can see that this position here is the opposite of this position. That's why sometimes You'll hear in the engineering discussions, you'll say it's it's 180. Out. Arts, it's it's it's phase shift is 180.

That means it's the same, but it's the opposite. Um, for instance, and again, just real quick up here, if I've got a sine wave, all right, well, that's going plus and this one's going negative, the amplitude of the distance between the zero line might be the same. But we're going in the opposite direction. So it's opposite. And we'll leave it at that. I mean, I don't want to get into AC theory at this point, that's another module.

So when I say 180 degrees, we think about the opposite. 270 is a right triangle, but it's going negative. It's going down. Here, and then we're back to zero or 360. So 360 and zero are the same point on a triangle. All right.

So let's move on. All right, well on a right triangle, and we're showing you two here. There's 180 degrees, and a right triangle. And this is what I mean by that. Okay? We know that when I have a right triangle, and this side and this side meet that's 90 degrees.

All right. So if this angle up here is 60, then this angles got to be 30. Same thing over here, 90 degrees, right triangle. All right, when we have a right triangle, there's always We always have an angle of 90 degrees. So right here, I've got an angle here of 45. And this one I've got 45 degrees because 90 plus 45 plus 45 is 180.

So again, there's always 180 degrees in a right triangle. So the example here is okay, what's this angle? Well, if I this is 90, and I give you the angle up here, which is 40, I can solve for that angle is going to be 50. Because 180 right. The angle in a right triangle is 180 minus 90 here, minus 40. there if I do the math, it's 50 degrees. So that angle here is 50 degrees.

That's it so I can see if I have a right turn. I know and I know two of the angles right now I can find the angle of the unknown, or the unknown angle. All right, on this slide here, we're gonna we're still talking about a right triangle. In the previous slide, we spoke about angles. How how there is a, a right triangle, there's 180 degrees. In other words, all the angles in the triangle equal 180 degrees.

On this one here, we're going to talk about the area. All right? And there's a formula that was created by a Greek mathematician many, many years ago, and it's called Pythagorean Theorem. And it's right there and why doesn't my pen work? There we go. We call Pythagorean Theorem.

And here's the formula here and I'm going to explain that and then minutes is c squared equals a squared plus b squared. Well, over here in my triangle, we have three sides, as you know, we call them side a side B inside C. And what we're saying is the area. And if you remember, an area of a square is the length times the width. All right, since this is a square, the length equals the width. So that's why we have area equals a squared over here, and area equals b squared over here, because it's a, it's a square, and all sides are equal. So we're saying here again, the area of a squared plus the area of b squared equals the area of C squared.

There it is right there. Area C squared equals a squared plus b squared. Now, the leg of the triangle that we call C has a fancy name called high pot noose right there. All right. And when we're dealing with electronics and analysis of AC circuits, okay. We use this quite frequently, when we want to calculate resistance and reactance in an AC circuit.

When we get into again, AC circuit analysis, which is not part of this, this lecture or this course, okay, we'll see that current and voltage are out of phase. In other words, then they don't follow the, the patent code identically. And again, that's all I'm gonna say, cuz we're going to go off on a tangent, I don't want to go there. So what I'm going to say is, the reason we teach right triangles and true trigonometric functions, is we use that in the analysis of AC theory, AC circuit analysis. All right. So I think even a couple of three or four slides, I do one for do one or two of them, where we talk about reactance is of resistance and we'll see when we get there, but that said, so again, getting back to this slide, if I want to find See, or the let them see.

I say C equals this A squared. plus b squared, I add them. And then I find the square root of that. And I think there's probably an example on the next slide. So if you need to watch this slide again, there was a lot in here, ah, this is called Pythagorean theorem and the C side of the triangle, okay, opposite this side opposite the 90 degree angle is called the high pot noose. All right, I'm on this slide here.

We're going to give you an example of finding the length of C right there. And again, we're showing you the formula right there, see equals a squared plus b squared, and then we find the whole square root of that. So I gave you square a is three b equals the length of four. So again, all we do is we plug them in. So a squared is three squared. b squared is four squared, and then we square them.

And we find that three squared is nine and four squared is 16. We add them which is 25. The square root of 25 is five. So therefore, C equals five as we show here, through this through this process, okay, so that's it, um, and let's go on. Okay, I threw one more in here just to explain. So, if you look here, we want to still want to find see and we have side as well.

10 Units long inside vs 10 units long. So again, we're saying a squared plus b squared. So we're saying 10 squared plus 10 squared. And we happen to know that 10 squared is 100. And I didn't I didn't show that. But if we wanted to put this in here, right there, it would be 100 plus 100.

All right, and then we come back in, so we add them. And it's 200. The square root of 200 is 114. point four. So therefore C is 14.4. I'm sorry. 14.14 units long.

All right. So um, what I didn't show you there is this Step, but again, if we square 10 squared plus 10 squared is 10 squared is 100. So we've got 100 plus 100. There, and that equals 200. All right. So that's it on this recording.

We're going to talk about finding site A and B in the next next portion of this lecture. We're going to stop this section right now. Okay?