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Hello all right we're going to do section eight — pile of signs goes on the bottom out of that enzyme can turn into flips and consonants loves 8-5 lost signs and law of cosines oh so little let's take a roaches on a cheese on ashes at an auto-repair read listen ah there we go first we start with the law of sines I'm going to write in cursive because it makes me look very elegant and formal was free I put an s on that for some reason law of sines I'll put a heart there just to make you cheer up a little it's just math calm down law of sines alright what the law of sines is it says it's essentially telling us a proportion that we can find in any triangle doesn't have to be a right triangle okay, so we'll do sine of angle an over its opposite side is equal to sine of another angle over its opposite side which is equal to sine of c over it's off the side he gets that a proportion with any of these you only need two to solve it but if you have three bits of information if you have like two angles and a side or two sides and an angle you can find it okay in any triangle didn't have to be a right triangle okay let's do an example just to you know get your hearts aflutter I don't use one on the books that's why I'm turning around 45 seconds a day okay we'll make this 105 32 and 18 right here let's say we want to find right here okay now all we got to do is set a proportion okay let's see we start with this angle sine of this angle over its opposite side which is 18 is equal to sine of this angle over its opposite side which is X the cross multiply would be x times the sine of 105 remember sine of 105 is its own number it's not sine times 105 sine 105 equals 18 times the sine of 32, and then we know that we have to divide sine of 105 on each side of your rid of it, so your answer is going to be whatever 18 comes sine of 32 over the sine of 105 now be careful when you put that in your calculator, so it's not to put the other sign inside the parenthesis, so I'm going to type it in and see if I got the right answer 18 times the sine of 32 closed parentheses divided by sine of 105 I got 9.875 blah blah blah and oh my goodness that's what I got about the block all right now we can move on to the next part okay that was law of sines what do you think comes next of you guessed it Clause comes yay cosines all right now the law of cosines says I want to redraw the things that I had said yeah I see hey hey hey BC all right now what it's saying is with any triangle like in this example two ABCs is had these side links you could set up this formula right here okay be a squared equals P squared I'm reading it because I don't know it memorized plus c squared minus 2bc, and you use this formula a lot in real life, so it's good, and it's good to have it memorized because I mean I'm a geometry teacher I've memorized I feel like I'm still okay hey is that for real that is awful I don't think that anybody should ever have to teach this because it's the most long and...
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