Hey, everyone. Let's take a look at this example. We have another triangle over here in which we're given 2 sides, b and c. And then the other angle that we're given is one of the corresponding angles or one of the corresponding letters. This is, again, a side side angle triangle. Let's go ahead and stick to the first steps over here, which is we're gonna set up a law of sines so that we can get an additional angle. Let's go ahead and get started.
So, this first step over here, we're gonna set up a law of sines. Notice how, again, the only two letters involved here are b and c. So when we actually set up our law of sines, we'll completely disregard the A term because we don't know anything about A or little a. So in other words, we just have Bb equals Cc. Alright?
Again, what happens in these problems is you're gonna have big B over here, and little b and little c, so you can go ahead and solve for C. That's going to be that second angle that you find. Okay? So what we're going to do here is once we cross multiply, move this to the other side, we're going to see that sinC is equal to 2 times the sinB, which is the sin of 29 degrees divided by little b, which is 4. Now if you go ahead and work this out, what you're gonna get is you're gonna get something like 0.242. And whenever you do these problems, again, I like to hold on to a few more decimal places because otherwise, you get some rounding errors. But when you solve for this, we're gonna see here is that we get 0.242. Remember for the first step, if you ever get something that's larger than 1, you're gonna have no solution, but that's not what happened here. Right? So we actually are gonna get something that's less than 1 or equal to 1. We move on to step 2, and we're perfectly fine to continue the problem.
The second step here is we're gonna use the inverse sine to solve for 2 possible angles here. So what's going on? Well, basically, what happens is if we solve for C, remember, we can take the inverse sine. So we're just gonna take the inverse sine of 0.242, what you're gonna get here is you're gonna get the inverse sine is equal to 14 degrees. But that's not the only angle that when you plug it back into sine, you'll get this number for. So that's actually where we sort of split our problem into two parts. So, basically, what happens is that C1 is equals to the inverse sine, which is 14 degrees, but C2 is just equal to 180 minus C1. Right? So in other words, it's just minus the angle that we just found over here. So it's 180 minus 14, and then C2, therefore, is equal to 166 degrees. So we've got these two different angles over here that when you plug them both back into the sine, you could double-check this, you'll actually get back to 0.242.
Alright? So how do we figure out which one is possible? Well, actually, that leads to the third step. So after we're done with step 2, we're gonna see that we have our 2 possible angles. And by the way, this didn't happen over here, which is that the sin of the angle is equal to 1. So again, this may happen, but it's rare. We're just gonna keep going on to step number 3. So, for step number 3, what we're gonna do is for this angle here that we just calculated, the second one, we're gonna add it to the given angle that we have, and there's a really good reason why. So here's what this means, add to the given angle. The only other given angle that we have is the fact that B is equal to 29. So what does this mean? It means that if you add B+C2, and this is just gonna equal 29+ 166 degrees, so 29 degrees plus 166 degrees. If you work this out, what you're gonna get is that this is equal to 195. But how is it possible that two angles in a triangle add up to something that's greater than 180 degrees? That's im 해결합니다