Hey, everyone. Welcome back. So we're going to spend a lot of time in this course talking about angles and triangles. And I want to give you a really good solid foundation for this because we'll be talking about them a lot later on. So in this video, I'm just going to walk you through a basic sort of refresher on the basics of triangles. There are a couple of important conceptual and mathematical things you need to know, and then we'll do some examples together. Let's get started here. A triangle is really just a geometric shape with three sides. That's a really sort of basic definition over here. All these things here have three sides, and they all sort of close together to form a shape, and that's a triangle. Now, there are actually three types of triangles that we can classify based on the lengths of their sides. This is just some vocabulary that you'll need to know. Alright? The first one is called an equilateral triangle, and this is where, if you'll see, all the lengths of the triangle are the same. All of them have a length of 3. Equilateral just means that three sides have equal length. That's actually what that word means. Alright? The way that we indicate this in diagrams is you'll see these little tick marks next to the numbers. That just means that those two or three measurements are all the same. That's an equilateral. An isosceles triangle is the next type, and this is where actually two of the side lengths have equal length. Notice how the bottom side is 3, and these two top sides over here are 5. That's an isosceles triangle. The last one is called a scalene triangle. This is where actually none of the sides have equal length. Notice how this is a 3, this is a 5, and this is a 6, so you'll see no tick marks anywhere. Another way of saying this is that all the sides are different in the scalene triangle. Alright? That's really all you need to know about their sides. Now, whenever sides meet in a triangle, they actually form angles. So the way we indicate this is by using a little curved arc symbol over here, and we express that angle in terms of degrees. So wherever you have two sides of a triangle meet, they form angles, and there are three other types of triangles that we can classify based on those angles. Alright. So again, this is just more vocabulary over here. An acute triangle over here is one in which all of the angles are less than 90 degrees. All of these words that you'll see acute, obtuse, and right have to do with what those angles are relative to 90. So look at these angles over here. All of these things are less than 90 degrees, so this is an acute triangle. Alright? So this next one over here, you'll see that there are two angles that measure 35 degrees, but there's one of them that measures 110. And this is an example of an obtuse triangle because one angle is greater than 90 degrees. So that's an obtuse triangle. The last one is called a right triangle. We're going to spend a lot of time talking about these, and these are special triangles where one of the angles is exactly equal to 90 degrees. Alright? Now, regardless of any type of triangle, whether we're looking at the sides or the angles, one really important thing you need to know is that in any type of triangle, all angles will always add up to 180 degrees. That is a fundamental property of triangles. So you would look at all of the triangles over here, all these three numbers will add up to 180. Same thing for this and same thing for this. Alright? So that's really important because if you know that all of the angles add up to 180, if you're ever missing one of them, then you can always find the other one. Alright? So that's actually really important. Let's go ahead and take a look at our first example over here. We're going to, for each of these triangles, figure out the missing angle or the missing side. Alright? So in this case, over here for this first example, we have a missing side represented by a variable over here. This is x. How do we find that? Well, we haven't discussed any mathematical ways of calculating this, but one of the things you can notice here is that these tick marks mean that the measurements have to be the same. So in other words, if the left side is 4, then that means that this also has to equal 4. Alright? So that's just something that you might need to know. Let's take a look at the next one, example b. This is one where we have two of the angles. This is 40 degrees, 40 degrees, but we're actually missing one of the other ones. How can I find that? Well, again, remember, all of the angles have to add up to 180 degrees in any triangle. So if you're ever missing one of them, you can always find the other. I'm just going to set up a simple equation over here. This is going to be 40 plus 40 plus theta. So, in other words, if I add up all of the angles, I have to get 180. If I just subtract 40 from both of the sides over here, this is basically the same thing as subtracting 80. What we're going to find here is that this angle is equal to 100 degrees. Alright? So this angle over here is 100 degrees, and therefore, this would actually be an obtuse triangle, but that's not what the question asked us. Alright? But that's the answer, theta equals 100. So that's it. That's just a basic introduction. Let's go ahead and get some practice.
Table of contents
- 0. Review of College Algebra4h 43m
- 1. Measuring Angles39m
- 2. Trigonometric Functions on Right Triangles2h 5m
- 3. Unit Circle1h 19m
- 4. Graphing Trigonometric Functions1h 19m
- 5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
- 6. Trigonometric Identities and More Equations2h 34m
- 7. Non-Right Triangles1h 38m
- 8. Vectors2h 25m
- 9. Polar Equations2h 5m
- 10. Parametric Equations1h 6m
- 11. Graphing Complex Numbers1h 7m
0. Review of College Algebra
Pythagorean Theorem & Basics of Triangles
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