BYU-Idaho Online Learning
Video Transcript
[This transcript is currently a work in progress.]
FEMALE: Okay. The side, side, angle situation. It is what's called the ambiguous case. And the reason why it's called the ambiguous case is because it actually creates four different options. Okay? Now, it's not required, but it's strongly suggested that you draw your triangles in the way that I'm going to demonstrate right now. So what we're given is we're given a side, a side, and then the angle. So we're given something like alpha, side A, and maybe side B. So side, side angle. Now, there is a reason why I have not drawn this connecting angle. It's because I don't have enough information that's given to actually tell me if I even have a triangle. Okay? So when we look at the side, side, angle situation, there's four cases that come about. And in the PowerPoint, they're going to introduce those four cases and help you understand them. So I'm just going to briefly introduce them and get you started with them. Okay? And then do hopefully one example. Case 1. In Case 1... If... side A is greater than or equal to side B, there is one triangle. And we just use the law of sines. Okay? So we sketch and we say, "oh, A is bigger than or equal to B, we use law of, law of sines. Ready to go." Case 2. Oh, by the way, let me make mention of this. I do this in a different order than the book. The order doesn't matter, but Case 1 is a pretty quick, easy, look and tell if I got it; Case 2 through 4 requires you to find the height, and so that's why I do Case 1 as Case 1. So we find the height. Now notice that I found a right triangle, so, I can use my right triangle tools. I can say, "sine of alpha equals H over B," and so the height is equal to B times the sine of alpha. Kay? So I've made a right triangle, I can find out what the height is. If the height is bigger than side A. So this height is bigger than side A, well, then there's no way A's ever going to make it to this other side. There is no triangle. And every student who learns this are like, "can we please have all of our problems like that?" Because that's super easy to work with. Unfortunately, no. Case 3... if the height is equal to A. So if the height and A are the same, well then, side A is actually sitting right here on the height... There is a right triangle. And I'm actually almost done solving it, and I can use my right triangle tools.
[End of video.]