okay so right now ladies and gentlemen give in 58 degrees B equals twelve point eight and a equals eleven point four all right so let's go and draw the triangle like we would any other time so I could say here's a which is at 58 degrees all right here's C and we'll call this one B C we don't know any information for B we know this is twelve point eight and a we know is eleven point four right so automatically ladies and gentlemen you can see that I have side side angle all right when you have side side angle rather than just following your daily tasks that you do every single day I kind of want your ears to perk up and say all right now is a possibility that I have two cases all right because what we need to be able to do is there's a possibility now that I could have multiple triangles alright and here's what here's the case the reason why this isn't really a great triangle I could actually even shorten this up but what I could what I'm trying to show you guys is you could have a triangle that looks like this right couldn't you also just draw the same triangle if you kind of use this as a hinge and it went right there right because we don't know what angle C is right so my angle 11.4 could be here or probably a little bit or we could say eleven point four is here guess see how that's a possibility because we don't know what C is right now all we know is what these two side links are and yes I know my triangle isn't written because this side is much longer than this side and it's shorter but let's get through that but you guys see how I could have two possibilities yes that's like me hinging like that's pretending me like I took this like a hinge on a door and I like I rotated it down to here okay so it's kind of like the pathway of that side so you guys can see there's actually two triangles I could have an OP to I could have a triangle with an OP to C or I could have a triangle with it on a cutesy right so there is a possibility so it's not is it's not as basic it's just hey give me money take it back you know the stuff that we were talking about before so there's a possibility of two different triangles there's also a possibility what if 11.4 looked like that and let's say you know here's this side length is it a possibility that these could not even touch it is let's say if 11.4 is that long and then we end up finding C because we don't know what the length of C is what if C is short all right we'll get through that case right now let's just go and take a look at C I want you guys to understand there's a possibility of either two triangles one triangle or no triangles and this is always going to happen when we look at our side side angle so how does that work because we're going what you just told us to do is just find side side angle and so forth or define your missing angles well let's take a look at it so we have a ratio right we have a over a and we have a side length B so let's create the law of sines so we have 11.4 over the sine of 58 degrees equals 12.8 over the sine of b so we do our same thing we do our cross multiplication and we could say that sine of B is equal to twelve point eight times the sine of 58 degrees all over eleven point four I'm solving for B so I multiply cross multiply to the night divided by eleven point four so I can do 12 point eight times the sine of 58 and then divided by eleven point four so I could say the sine of B is equal to 0.95 to two all right now ladies and gentlemen make sense for that to be an angle right you got to take the inverse sine correct right so you take the inverse sine of your second answer and you get 72 point two one degrees so we say B equals sine inverse of 0.9 0.9 five to two and we could say B equals seventy two point two one degrees okay so here's where it's going to get a little dicey so let's go back to the unit circle all right what I did is I just found the inverse right I apply the inverse and the important thing for you guys to understand about the inverse is if I'm going to look at let's say I have a signed value let's look at the sign value of 1/2 if I say the sign of B equals 1/2 is there one answer or two answers to that there's to it because what is what is is sign equal to one half at PI over six yeah of course it is and it's also equal over here right so if I was going to say sign inverse B of 1/2 we could say B equals PI over six and five PI over six right because your sign is positive in the first and second quadrant so therefore there's two actual answers we could say here it's PI over six which is your reference angle notice these are your reference angles but this angle right here is five PI over six right so does every wonder stand what I'm taking the inverse of my sign I'm my domain I'm going to have two values that are in the first and second quadrant I have that I have my original angle and also using it as a reference angle so what I want you guys to understand is if I'm going to look at 72 degrees with my market up go so if I'm looking at 72 degrees and I say if I say the inverse of point nine five two two two is giving me 72 degrees which is right here do you think I'm going to have another angle that's going to have that exact same sine value yeah I'm going to have the one over here right so what would that angle be how would how could you we know this angle is 72 point two one how can I figure out what that angle is close not exactly 90 but if we take 180 minus that will get what this ain't will get that will get the remaining angle okay so let's go and take so let's go and take 180 minus our angle seventy two point two one and what that gives us is B is going to could also equal 107 point seven nine okay so we're not done yet yes what do you mean this one here know this from here to here is seventy two point two one degrees so we want to find what that angle is so we're taking 180 minus eNOS and that's going to give us that angle well I'm not done explain I'm still going to kind of go through it do you kind of understand though how there's two different angles that have the same time value okay do you understand here how these both have the same sine value 1/2 and 1/2 right so same thing with this if I give you one angle you know there's an opposite one that has the same sine value right these two angles are going to I don't know what their coordinates are but they're going to have the same sine value right so if you find one you got to make sure you check with the other one because there's going to be two in the first and second quadrant okay so you got check two angles we're going to go through now don't do both of these triangles do both of these angles work so that's what we do is we say we create case one and case two so right now we have B equals 107 degrees so we could say B equals 100 seven point seven nine degrees or we also said that B could equal 72 point two one degrees so there's a possibility now there being two different C values and let's go and see if these work okay so what we do is we write case one case two so case one says that let's do this is case one and this will be case two so case one says this is seventy two point two one degrees that's an acute angle right so we could say that's going to look something like this 58 degrees that's going to be something like this so this would be seventy two point two one and they're gone this is oh wait did I get them to be the same oh yeah I wrote it in there didn't I okay yeah we said that's could be seventy two point two one or we could look at case 2 which says it's going to I wrote in I wrote in case number one we don't know that that's one example right we don't we don't actually know what this angle is right now I wrote in what B was and I wrote in what a okay we don't know what C is though right now Mackenzie let's go and take a look at this one so if I say now B is equal to 102 degrees so I still have 58 degrees what you guys need to understand is do do you understand when I was taking well first of all we have side-side-angle do you know in the other ones I wasn't using the inverse sign right when you when you complete the inverse sign that's what's giving you your two options right because you have when you complete the inverse sign you know that you have to be able to find both values that's why that's right drop the unit circle when you apply the inverse sign you have to understand that there's going to be two possibilities in that first and second quadrant right that's why we come up with this case so what did I find a B so we said B could equal 107 degrees all right so now what I want to do is I want to see do either these both work I know it's not work so let's go and take a look at case one this case one does this work if I'm given a and B can I figure out what C is so 180 minus 58 degrees right we are given 58 degrees from the beginning and then - our new angle seventy two point two one is that going to give us our new value equal to C so what will now angle C equal right because on my case one I figured out what B was 19 I can figure out what C was so we do 180 minus 58 minus 72 points to one and that gives me yeah hey C is going to be 49 point seven nine degrees okay oh it's just 7.21 okay let me go and change them 180 minus 58 mine oh I did it right I don't know why I wrote that in there all right so now that's for case one what about if case - what if we said now hey this is going to be a hundred seventy degrees this is 58 degrees is it still possible to create this second triangle so what I do for this see as I do 180 minus 58 degrees minus one hundred and seven point seven nine degrees equals C so we do 180 180 minus 58 minus one hundred seven point seven nine you guess what I get fourteen point two one so I could say fourteen point two one degrees equals C and I know my triangles kind of looking a little crazy guys it would probably just be something like that all right so we could say this angle is fourteen point two one so you guys see how I can create count atutor trial here's where it's obtuse here's where it's acute but there's two possibilities and I can still remain that I can still create the same so we know a is eleven point four B is twelve point eight so the last remaining value is we need to figure out what our C is so we're going to use the law of sines for each value to find our value C so for this one I don't know I'll use a so I'll do eleven point four over the sine of 58 equals C over the sine of forty nine point seven nine that's for case one for case two I'll do the same thing eleven point four over the sine of 58 degrees equals C over the sine of fourteen point two one alright and then I'll cross multiply and divide I'm just going to kind of do this to speed this along so my last one for case one I'll do 11.4 times the sine of forty nine point seven nine and then I'll divide that by the sine of 58 and I get C equals ten point two six for this case I'm going to do 11.4 times the sine of fourteen point two one and then divide that by the sine of 58 degrees and here I get C is going to equal three point two nine okay so ladies and gentleman the main important thing you guys need to take from this all right I know it's a lot of extra work you're looking at you just need to take this when you're giving side-side-angle and you have to you have to apply the inverse sine there's two opportunities you could have an obtuse or you can have any cute triangle you need to make sure you look into both of them next what we're going to do is look into what if there's no triangle at all all right and that'll be pretty simple that you guys will be able to see okay so this is your example yes I'll go over I'll show you on number five what exactly to do just want you guys understand get this so I'll explain number five here in a second I don't understand what