BYU-Idaho Online Learning
Video Transcript
[This transcript is currently a work in progress.]
[silence]
SIS R: When we look at this one here, couple things. You can only use right triangle information if you know you have a right triangle. There's nothing here that tells me I have a right triangle, so I've got to use one of my other tools. Since I'm given all three side lengths, that's a law of cosines problem. Now, as I've listened in on some of your groups, I noticed that we missed a big idea that I think is essential. So, with the law of cosines, I told you that you should always find the largest angle first, because the arc cosine is defined in the second quadrant, which is going to allow you to find any angle over 90 degrees. When I look at that and I suggest doing that, I'm not going to dock you for not doing it,
but I'll tell you this: that students who do not pay attention to that hint, and to their work, will inevitably make a mistake somewhere in finding the angles, okay? So it's super important that you think about which angle to find first. It's not a requirement, but just something to think about. So when I look at this, which angle should I find first, based on that hint?
FEMALE 2: It'd be gamma, because it has to, it would be the greatest angle.
SIS R: Perfect! Because it's across from the greatest side length. So we come in here and we set it up. So we get 10.8 squared equals 8.2 squared, plus 3.7 squared, minus 2 times the two side lengths... times cosine of gamma. Now, the second hint that I told you on the law of cosines is to remember your order of operations. And the reason why that's so important is because it's this guy right here, that I get all of this combined before we go after the cosine. And that would be incorrect, so really watch your order of operations. So I'd have to first subtract... the 8.2 squared and the 3.7 squared... And then, I can divide. Now, because I'm going to run it, well, nope, I got, I got it. So I'm going to have 10.8 squared, minus 8.2 squared, minus 3.7 squared, divided by this negative 2 times 8.2, 3.7, equals the cosine of gamma. Okay. Now. We keep asking this question, and it is essential that you understand why it's so important that I keep asking this question. So let me come up here. With the trig functions... Someone who has not talked yet today, what is my input? What is my output?
MALE 1: Input, angle; output, side length.
SIS R: Perfect! Okay. Someone else who has not talked yet today, tell me what the inverse trig functions do.
MALE 2: Input, side length; output, angle.
SIS R: Perfect. Now, we mentioned this on Wednesday, as to why this is so important, so, hopefully, after the second or third time, it's going to click now. When I come down here, this is not an angle. How do I know this is not an angle? Because those numbers right there all represented side lengths on my triangle, so I know it's not an angle. Second reason is that I've got cosine of an angle. So that means I'm inputting an angle and outputting a side length. Input an angle, output a side length. So if I'm trying to find the angle... then I must use an inverse trig function so that I can input the side length and output the angle. This is why, for the third or fourth time in this unit, I have talked about this. It is not just because I like to hear myself talk about this idea of input and output, but it's so that when you get to this part here, you go, "oh! I'm looking for an angle. I have to use an inverse." So we're going to have... Gamma equals the cosine inverse of that big number right there. Which all represents a side length. And I plug that through, and I think, Group 4, you guys came up with the gamma, didn't you? Would you unmute yourself and tell me what you got? Or someone? Tell me what you got for gamma?
ELI: 126.05 degrees.
SIS R: Perfect. And Eli, thanks for going two decimal places. At all times, go at least three decimal places when you're doing this. Now that I have gamma, I can come back up here and I can use law of sines and I can figure out the rest of it. And I'm not going to take time to do that because we need to switch gears and talk about a couple other ideas. But I wanted to go through this to talk about the two hints. Always find the largest angle first, because the arc cosine will be able to find any angle over 90 degrees and really watch your order of operations, okay?
KATYA: Sister R?
SIS R: Yes.
KATYA: Can we, like, in the... problem we just did, could we use cosine and then switch to sine?
SIS R: Yes, and Katya, a lot of students will do that. So as soon as they find that largest angle, because you're only going to have one angle over 90 degrees. So soon as you find that one, I would suggest switching to the law of sines and finding everything else that you need.
KATYA: Okay. Thank you.
SIS R: Yep. You bet.
[End of video.]