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9.4 & 9.5 Notes for Reg Geo

Added Mar 28, 2016 •

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we're going to do 9.4 9.5 together because it's all trigonometry right triangle this whole chapters about right triangles so the trigonometric ratio all trig is making ratios out of the sides it's the ratio of the length of the Sun of a right triangle now we have three main ones that we're going to use there are more but these are the three we're going to use and they are sign sign in Tangent for short sign is sin cosine is cos and tangent is tan now you'll notice if you look calculators you're going to see these three buttons on your calculator sine cosine and tangent and that's what we're going to use today no tricking it up trigonometric ratios are lighted to only the acute angles of a right triangle and not the right triangle you will never use the 90° angle to do this but we have to have it to show that we have a right triangle so we're only going to use angle B and angle a in this triangle to do trig ratios with okay so these are your three trig ratios right here and you know it's signing cosine and tangent of a now that's important because angle a or angle B but for this I'm going to show you everything with regards to angle a now in this triangle we have three sides we have hypotenuse which is going to be seeing this triangle and then we have the two legs no it depends on which angle you're using the way that we Playbar legs if we have a leg that is opposite in a leg that is adjacent opposite would be across so this is going to be our opposite and remember Jason is always touching so the side that is touching the angle we're using is always going to be our adjacent know if we used angle these two would be switched this would be opposite in this one would be the adjacent to learn how to do this definitions so the definition of sign is the opposite leg  over the hypotenuse that is your ratio so in this case the opposite leg here is a and the hypotenuse is C we would put a oversea in those would be numbers you could be 5 or 6 something like that okay the cosine is the Jason Legg  over the hypotenuse  and in this triangle the adjacent is in the hypotenuse is C so it's going to be be over sea  tangent tangent is the opposite leg over the adjacent leg and I'm abbreviating here so the opposite of a would be play in the adjacent would be be so it's A over B can I know there's a way to remember which one is with there's a way to remember sine is opposite over hypotenuse cosine is adjacent over hypotenuse and tangent is opposite over adjacent and that's what you need to know now are on your phone and you will be able to use that but sohcahtoa is one way to remember this and the way that we use that is so remind us that sign is opposite over hypotenuse the part of that reminds us that cosine is the adjacent hypotenuse  and the TOA reminds us that tangent is off over adjacent so sohcahtoa now there's another way to remember if you can't remember the order of this sohcahtoa some old hippie caught another hippie tripping on acid and just a funny way to remember it's not a big deal but there's all kinds and you can make your own if you want to  okay simple when it says find the sign of a cosine of a tan of a sign of a cosine B&B Express each fraction gear ratio in decimal this will be just like some of problems in your homework all I want you to do is set up which side over which side finally ratio that's all you have to do solving anything just yet so if we are using angle a first so we can find the sign of a the cosine vandetanib a label your sides this will be the hypotenuse no matter what because it's across from the night now with regards to angle a opposite would be right find a Jason twould be the side or leg that is touching a so this would be my adjacent side soap sign is the opposite 5 over the hypotenuse 13th should be 5 over 13 now if you change turn decimal 4/13 you get Point 3846 and we're going to go to four decimal places for this alright cosine of a sign is the adjacent 12 over the hypotenuse 13 so that would be 12/13 or .92 three one pause this video as much as you want and Rewind  now let's do the tangent of a tan is opposite 5 over adjacent 12 so that would be 5:12 or if you type that in your calculator point for 67 we want to do the sine of angle B the cosine of angle B and the tan of angle B so were using a different angle this time were using beat now that does not change my hypotenuse it off but it does change my opposite and adjacent if I'm doing opposite of the it becomes the 12 now so now this is my opposite and now is my adjacent because it's touching be so she's going to flip those two sides so when I go to do sign now sign of angle is opposite 12 over hypotenuse 13 so it's 12 or 13 or 9231 cosine of B is the adjacent 5 over the hypotenuse 13 so 5/13 or .3 846 and then tangent of the is opposite 12 over in Jason 5 so that's give me 12 / 5 4 - .4 rounds off to know if you'll notice sign of a and cosine of B are exactly the same and cosine of a inside of beer exactly the same because depending on which angle it flips the opposite and adjacent and you're still doing it over the hypotenuse how to evaluate trigonometric ratios you can use a scientific calculator now if you don't have a scientific calculator at home can use your phone if you'll turn it sideways those buttons should pop up when you turn it your calculator sideways or there is a hundred free scientific lighter apps that you can download and I suggest you download one if you don't like it delete it try another until you can find one but the biggest thing no matter what cow later you're using is you must make sure that your calculator is in degrees show on the ones that we have hit the mode button make sure that degrees is highlighted and not radians now on any other what you later there might be a button that says deg 4 degrees and RAV4 radians you always want to make sure it's the degree one okay or you're going to get the wrong answers all you have to do here his toughness in your calculator find the value using the calculator the sine of an angle that's 49 degrees will always be a number a certain ratio and it's always in a fraction form in your calculator but all you have to do is hit that sign button and it prints you open up 1049 close the princy hit inner you should get .75 for 7 if you're not getting that go back to your make sure you're in degrees k type in the tan hit the tan button and then type in 82° close your parentheses and you should get 7 11544 cosine of 3 degrees you should get .998 six and four sign of 87 you should get .99 86 now why are these two equal well what is 3 + 87 that's 90 degrees so these are the the same triangle if these two out of 290 that means they make a triangle together so that's why they're the same one sign of one angle and ones cosine of the other just we did at the top  okay now we're going to use all of that to solve for a part of a right triangle so what we're going to do who is look at what we're given right here we need to find know it all depends on what angle were given this one is 31 lyrics to use this angle and if we use that angle of course this is my hypotenuse and then from there this side is opposite and this side is the adjacent because it's the leg that's touching the 31 so this one is the adjacent no they give us the opposite side and we need to find the adjacent side so those are the two sides that we need to use in our no opposite and adjacent look back at your sine cosine and tangent in which one involved opposite and adjacent both of them and you'll see that it's 10 so what you do is you do tangent of the angle remember it was it a will my angle is 31 degrees equals the opposite side 24 over the adjacent side x now when we go to solve this basically what you're going to do is you're going to put this over one and you were going to multiply on the bottom let me show you a shortcut I have a ratio equals a ratio this cross can be so what we're going to do is we're going to switch these two spots in this is when the x is on the bottom that you can't just multiply so what you play Wiz you put the X where the tan of 31 is equals 24 stays and then I'mma put the tan of 31 where the X was now I've solve for x so all you do is type in your calculator 24 / hit the tan button 30 Vickery's close your princi hit inner what you should get is x equals 39 and we're going to round to the tenths place point so this equals 39.9 this access  you need to go can you watch that again do that let's look at F K they give me this angle right here so with that I have the I did is adjacent and I have the hypotenuse so these are the two sides I want to look for sine cosine or tangent uses high Nina Jason it's cosine so cosine of your angle 47 degrees equals the adjacent turn over the hypotenuse D now again D is in the bottom all I need to do is switch these two how to make my ratio so the deed goes here 10 / cosine 47 degrees tightening your calculator exactly like it looks 10 divided by cosine 47 and you should get D equals 14.7 so this hypotenuse is 14.7  G you noticed we have an n and an m 4K  so we need to find this in and we need to find this m  well play more sides we know that this is my hypotenuse and if I'm using this angle this is adjacent to it it's touching it and this is opposite to it depends on which one you want to find first let's say want to find in first so let's find in in is the opposite and I know the hypotenuse you have pick a side that you know to go with it so which one is opposite and hypotenuse that is fine so sign of my 72 degree angle what's the side that's opposite in over the hypotenuse 50 now this time when I put it over one cross-multiply those cross and they multiply what's your variable is in the top all you have to do is cross these if your variable is at the bottom like this one that's when you have to switch the two so the variables at the bottom you switch up if the variable isn't the top like this one all you got to do is cross multiply so end times one is in my other cross is 50 times the sine of 72 degrees all you do is type that in your calculator exactly like it looks 50 hit your sign button 72 closure parentheses and you should get 47.6 so now I 47.6 year now if you want to use that side to help fun M you can do that I'm going to go ahead and use the side that I already have now I want to find him this time is the adjacent side and I mean use my hypotenuse cuz I already know that's 50 you can use this one so Jason and hypotenuse adjacent and hypotenuse is cosine so I'm going to do cosine of my 72 degree angle Jason to that is M and the hypotenuse is 50 now again when I put that over one that cross multiply so all you have to do is multiply now so m equals 50 times the cosine of 72 degrees typing in your calculator exactly like it looks 50 time cosine of 72 and you should get 15.5 so this site is 15.5 in now I know every side of my triangle I want you to try to work this out all by yourself and then start the video again and see if you got them all right  sofurry for a you should have gotten 13.1 if you want to see how I did it it's right here and B you should have got 30.9 this is how I did it you did not have to do it exactly like I did as long as you got the right answers your good okay alright your homework what's the worksheet get it done and we'll have a quiz next time over this

Uploaded by Pam Chastain.

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9.4 & 9.5 Notes for Reg Geo

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