Everyone, so in a previous video, we discussed the basics of triangles, and I mentioned that we would very commonly be working with right triangles. But one of the most common situations that you'll see is where you have two sides of a right triangle that are known, but you have an unknown side. So for example, we have 3 and 4 that are known here, but this side x here is missing. Well, don't worry because in these kinds of situations, we can always solve for this missing side by using something called the Pythagorean theorem. It's probably something that you've heard before in a math class, but we're going to be using it a lot in this course, and you'll need to know it. So I'm going to go ahead and explain it to you. What I'm going to show you is that it's really just an equation relating the three sides of a right triangle. Let's go ahead and get started. We'll do some examples together. Alright?
The first thing you need to know about the Pythagorean theorem is you can only use it when you have a right triangle. Alright? So, you can only use it when you can assume or when you know that one of the angles over here is 90 degrees. If you don't know that, then this equation won't work. So what is the equation? Well, it's really just a2+b2=c2. Again, you've probably heard that before, but what it really means is if I take these two numbers over here, a and b, they'll just be numbers, and I square them and add them together, that's the same exact value as this side over here squared as well. Let's take a look at our first example, so we can actually just get some practice with this and do it together. Alright?
So we have 3 and 4 that are known over here, and you have x that's unknown. This is a right triangle, so I'll be able to use the Pythagorean theorem to solve that missing side. I just have my equation over here, a2+b2=c2. Alright? So how does this work? Well, what's really, really important about the Pythagorean theorem as well, is that you always have to keep in mind, take notes that your a and b need to be the shorter legs of the triangle. Always set your a and b as the shorter legs that form the corner, that form the 90 degree angle, and then you want to set c as the hypotenuse. The hypotenuse of a triangle is always the longest side, which usually is going to be the diagonal. Not always, but it's almost always going to be the diagonal one. Alright?
So in this right triangle over here, what we can see is that these two form the sort of corner like this, that's a and b, and c is going to be the diagonal, the longer ones. That's what we set as c. Now, when it comes to a and b, it actually doesn't matter which one you pick as a or b. I'm going to go ahead and just pick this one as my a and this one as my b. So what this equation says is that a2+b2=c2. So in other words, if I take 4 and I square it, and I add it to 3 and I square it, and I figure that out, that's going to give me this missing side squared. That's going to be x2. Alright. So 42+32, this actually just ends up being 16 plus 9. That's going to equal x2. And if you actually just go ahead and work that out, that's going to be 25. So are we done here? Is the answer just 25? Well, no. A lot of students will mess this up. You