hello and welcome to another Ginger math petition video where I'm going to go through a long video here on igcc questions on trigonometry skills so if you really want a crash course in how to use the sign rule the cosign rule using soaka TOA in a long extended kind of question and this is the video for you before I get started then do think about liking and subscribing this has come directly from my channel so I sent out a poll and said what kind of video do you want me to do in my all of series and the Very first thing that came up was s and cosine rule so let's get started and do some of these questions now remember you have a formula list so we're going to use these formula at the bottom a lot the S rule the cosine rule and the area of a triangle so I will be coming back to this through these questions okay so let's get started on question seven so AB is a vertical Tower of height 30 m they give us a nice diagram here and they give us an angle a BCA 68 de and BD is equal to 36 M and we need to calculate a d now one of the things I notice students do is they look at this kind of question they go right I have to use trigonometry I need to use trigonometry but let's consider this a bit more carefully we actually have here a right angle triangle this is got a 3D representation but it is still essentially just a 2d right angle triangle so I'm drawing this over just so you can see what what I'm highlighting here and if I draw this in 2D so if I just do a very quick 2D sketch not to scale of course then notice this here is 30 m this here is 36 M and then we're looking for this side here once I draw it like this then actually we don't need trigonometry here at all despite the title we can just use Pythagoras now the way I recommend to year 11 students is that you can get the two method Marks here with a very straightforward calculation we can do x equal we're going to go the Square t of 362 - 302 so we can write this as one very smooth calculation if you want to use Pythagoras directly then we could write this as 362 uh equals sorry x^2 + 302 rearrange this so we get x^2 = 36 2 - 302 and and then do X is equal to the square < TK of 362 - 302 we want to show all those steps in working but if you look at the Mark scheme you'll see that this is perfectly adequate to get the two method marks now once we've got that then we're going to have to work this out on our graphical calculator so we type this in so control uh this button here for the square root 30 6^ 2 - 30 SAR press enter and then we get our answer of 19. 89 so I'm going to write that here 19.8 9 dot dot dot and remember for all these questions we're going to do here we always round to three significant figures so this is the first significant figure second significant figure third significant figure so we draw our line afterwards and then the nine is going to round the eight up to 9 so we get our accurate answer here to three significant figures as we should always do of 19.9 like so and once we've got that then we're going to calculate the side AC and show that it rounds to 12.1 m round to three significant figures so they often like these show questions as part of trigonometry and this is a good examp example of this the three marks so if we go back to our diagram the side that we're looking for this time put this in Black here is this side here and again we've got another right angle triangle so if we draw a sketch out like so where this is a right angle this is 68° and this is 30 m notice we now do have a situation where we can use trigonometry and more specific spefically we can use socer TOA now if we're going to use socer TOA here the first thing we always always always do is label the sides so this is our longest side this is our hypotenuse this here is opposite the angle so we're going to put an O here and this here is the side we're actually looking for so I'm going to call it X in this case and this is the one that everyone forgets this is the adjacent so the side next to the angle and now we decide which side that we have and which side that we're looking to find so get the highlighter out here we are looking well we have the opposite and we're looking for the adjacent so in that lovely acronym we like to use so TOA which one has o and a in it which one has OA in it and that would be the last word that I mentioned there which is TOA now what does that look like well this is where I draw a formula triangle with a pen of course so here's my formula triangle I recommend you use this method we have tan Theta * a and o so you need to know these three formally triangles we're going to use through these problems and now because we are looking for the adjacent so we're looking for the adjacent side imagine that's crossed out we're going to do the C calculation o / tan of the angle okay so what what does that mean in this question well we're going to do 30 that's our opposite divided by T of the angle that's 608 so in order to show our calculation here AC is going to equal to what we just wrote 30 divided by tan 68 and let's go over to my calculator and work that out so before you do anything with trigonometry here make sure that it says de at the top for deg one of the biggest mistakes particularly International mathematics students 0607 students make it's on their graphical calculator they do not check that it says de at the top and not rad okay notice you can click and it can go between the two so once it's in De we are going to get the correct answer at this point we type in so 30 divided now to get the tan function you can either type in tan or you can press the trig button and you'll see they're all here for you so 10 60 8 enter and we get our answer of 12.12 so we're going to write that in so 12.12 dot dot dot and if we again round this to three significant figures like we've done in previous questions we get 12.1 M to three significant figures and I like these kind of questions because it's one of those show questions so in the exam I can guarantee I've got all three of these marks because I've written the working needed and I've got to the right answer that they've indicated to me in the question as well feel free to have a look at the Mark scheme so you can see where you pick up those method marks notice I picked up the M2 Mark here for the first question by writing it in one very quick calculation so I'm trying to save myself time through a very stressful exam whether you're doing the paper for on 0580 or on 0607 it's still a good way of getting those method marks efficient ly and giving yourself more time for other questions right and let's continue on to a more difficult star question now notice when you get a question number here on paper four with this is question 11 question 12 towards the end of the paper they generally are on the harder side whereas you're going to see later on question three that would be a slightly easier style question and we've got a triangle here and we need to use the cosine rule so we'll go back and check what the cosine rule is to show that this quadratic is true in some way so we got quite a lot of work to do here because it is out of four marks and let's just remind you what the cosine rule is so it's equal to c^2 = A2 + b^2 - 2 a b cos C now remember the marks the formula sheet actually had the letters in a different way around but let me just show you how these letters correspond to my diagram so the angle is going to be Big C so this one here the uh side opposite Big C is going to be small C and then the other two sides it doesn't matter which way around are going to be a and b like so so now I've labeled the side I can now substitute a b small C and Big C into my formula so I'm going to copy out the formula wherever I see a small C I'm going to put a nine wherever I see a small a I'm going to put a 3x minus one and so on so let's do that now so we get 9^ 2 = a 2 is 3x + 1 all 2 plus and this be very careful with brackets here so 2x all squar could squaring the whole of 2x here minus 2 * well a is 3x + 1 so 3x so minus one sorry can't read my screen that's not very helpful good I'm always checking these though so 2x times the cosine the angle well the angle is equal to 60 like so so let me change this because there should be a minus one here so that's important and now let's work some of these things out well 9 s is equal to 81 so that's fine 3x - 1^ 2 now remember that's the same as timesing it by itself so 3x -1 * 3x -1 and now we're going to use foil so that's first Outside Inside last to make sure we multiply it out correctly so 3x * 3x is 9 x^2 3x * -1 is - 3X 3X * -1 is - 3x and then -1 * -1 is + 1 make sure very careful with that last one there uh if we collect up the like terms then we get 9x2 that stays as it is - 3x - 3x is - 6X and + one stays the same so let's pop that in now so 9 x^2 - 6 x + 1 now 2x all s remember that's the same as doing 2x * 2X and that's equal to well 2 * 2 is 4 x * X is X2 so let's pop X2 here 4 X2 and now let neaten this out so here we've got two lots of 3x -1 multiplied by 2x multiplied by the cosine of 60 now this is one of these exact values that you should know off by heart of course you can always use your calculator to check this as well but the cosine of 60 is equal to a half now on a calculator paper this is obviously not that important let me just quickly show you so trig cos 60 is equal to a half so you can see you can use your calculator but if you know them it will speed up the process quite significantly so go times a half like so let's keep simplifying this down so 81 going to leave alone for the time being notice we've got a 9x2 and a 4x^2 so that becomes 13 x^ 2us 6 x + 1 and now we're going to work out the brackets so we'll do this in stages well 2 * a half cancels CU that becomes one so these cancel so we're left here with 3x - 1 multiplied by 2x just take it one step at a time and let's keep going so 81 = 13 x^ 2 - 6 x + 1 and now we're going to expand the bracket so I'll do this separately here so you can see what's going on so remember expanding a single bracket we used our single hook like so so 2x * 3x is 6 x^2 2x * -1 is - 2x so let's pop that in and this minus here is very important so we need to be very very careful how we deal with this and we're almost there we're almost there so once you see this Next Step you'll see what we've almost got to the answer so we get 81 = 13 x^2 - 6X + 1 and now we're expanding essentially a single bracket here as well with this minus so we get - 6 x^ 2 and this is the thing really to watch out for in this question the minus times a minus is a plus so we get plus 2X oh almost there so 81 81 hasn't moved for the time being so so 13 x^2 - 6 x^2 is 7 x^2 - 6 x + 2x is - 4x + one this is where you're feeling quite confident because this looks almost identical um let me just put the final answer up here bit of space so I'm going to flip over the equation so got all the x's on the left hand side and to get my very final Mark here where I want to have the right hand side zero so what's the opposite of adding 81 that's minusing 81 from both sides this is really satisfying when you get to this point and you get 7 X2 - 4x^2 + 1 - 81 is - 80 = 0 and the great thing about this is I know I've got the right answer you see this you see that and then you go yes I've done it I've got those four marks in the bag in this particular question which is a pretty tricky question it's certainly going to be great a for this kind of algebraic manipulation so you can have a look through the M scheme the M scheme is not very useful here because it doesn't show you all these intermediary steps that I did in the middle so this is why this kind of videos very very useful you can see exactly the process I've gone through to work out the answer right let's move on to another question 11 so two questions 11s and in the diagram ADC is a straight line now that is important a bit later on the first thing we need to do here is calculate a so as soon as you see this right angle triangle you need to be thinking Pythagoras or trigonometry here we have one side and one angle looking to find another side so trigonometry is called for once we know it's trigonometry then we have to label our sides so our first step that we do so this here this new X is opposite the angle so this is o this eight here is next to the angle so I'm going to put an a here again we use SOA so which of those has an o in it that's going to be tan again so we're going to use tan twice in this video so far again we need to know these formula triangles and this time we are looking for the opposite so this is the thing that we don't know so we cross out this part here and then we're going to do the calculation we see which which is tan of the angle times adjacent so to work at AB we are going to do tan 34 * 8 so I've shown my calculation for the method Mark let's go to my calculator and work it out so we're going to type in we can use T or we can press the t uh trig button tan 34 multipli by 8 enter and we get our answer of 5396 so I'm going to write down 5.3 96 dot dot dot again we want to round as always to three significant figures so 1 2 3 we round the nine upwards so that's going to give us 5.4 again we have to be very precise in the rounding that we do to guarantee that we get all the method marks now we need to work out the angle a DB C and it's a whopping five marks so you know there's going to be quite a bit of work involved in order to work out DBC now how do I know where DBC is well the middle letter always tells you where the angle is and the sides tell me okay how do I get there so d b c is going to be this angle that we're looking for here now back to my point here ADC is a straight line therefore I know that the these two angles so this angle plus this angle add up to 180 so to work out this angle here I'm just going to do a very quick calculation of 180 minus 34 and that's going to give me 146° so I'm just going to pop that in again always use a calculator if you're not sure about that calculation and then we look at the problem here and go ah well we've got a side and an angle we're looking for this particular angle here but at the moment we can't work that out directly however we can use this side over here we can use this eight to help us work out this one so if we go through the process again we have an angle and a side we have a side and then a missing angle here what does that call for here well there's no more Saka there's no right angle triangle so we're going to use either the sign rule the cosine rule this is a situation for the S Rule now what is the sign rule well uh this is on your formula sheet sin a over a equal sin B over B so we just need to label this up correctly just so we know which one is which so just to stop any confusion here I would rub that out but I can't so let me use a different color so we're going to make this our big a because we know we're going to make the angle that we don't know big a so they're going to make this one big a this makes this then small a and then we're going to make this big b and then make this small B if we label it correctly it makes the working we're going to do just now a little bit easier for us so let's go through this process so we've got sin a divided by the side opposite it that's the eight over here and that's equal to sign of the angle here so that's s 146 / 19 and generally when I have this kind of problem we want to try and get the A on its own or the sin a on its own so we look at the left hand side and go ah what's the opposite of dividing by eight well we need to multiply by eight on both sides this has the effect of canceling here so we get sin a is equal to A8 * sin 146 is exactly that divided by 19 and we can simplify this slightly further before we actually go on to use our calculator so then we have the sign of the angle so what's the opposite of signing well that's going to be the inverse sign and remember we do that to both sides so that's going to give us a because this part and this part cancel so we get the S inverse of 8 sin 146 over 9 19 and notice I haven't rushed to my calculator here until I've got it in a form that I like and try and minimize any of those rounding errors as we go through the problem so I'm going to go to my calculator and work this out so where is the inverse sign button where all you have to do is go to trig here and you'll find this sign minus one button under here so that's where our inverse sign function is to make a fraction we just go to control and divide that gives us our fraction and then we just type it in notice I can type in sin and It'll recognize the function do Love This Ti Inspire calculator and put 19 at the bottom if we work this out we get that angle of 13. 618 so let me write that in 13. 618 dot dot dot so that's the angle here 618 dot dot dot now of course that is not the answer that we're looking for here we are looking for the angle DBC but now we can use the idea that angles in a triangle add up to 180° so to work out this final angle so DBC we just do 180 minus the two angles that we do know so 146 + 133618 dot dot dot again trying to avoid those rounding errors by keeping as many decimals in as possible so let's go back to my calculator so all I'm going to do here I'm going to do 180 minus Open brackets 146 plus answer so control answer this allows me to get the most accurate answer possible for this particular question so if I work this out I then get my final answer of 2038 20. 38 do dot dot and of course we always round to three significant figures so our final answer will then be 20.4 de for our five marks now I think maybe this should be a four mark question personally but again there's quite a lot to consider here first of all the angles on the straight line then using the sign rule for an angle correctly and then realizing we need to use angles in a triangle to find our very final answer of 20.4 now we're going to use this a little bit in the next question as well so now we need to calculate the area of triangle ABC now just keep in mind here the triangle ABC so if I do this is a different color do some yellow is the entire triangle that we see in front of us so it's this part this part and this part here so we're trying to find the whole triangle together now the easiest way of doing this is to use that formula from the formula sheet that we haven't mentioned yet so the the area is equal to a half a b sin C where A and B are two sides and c angle is in the middle now the one that comes to mind here is to use some of the things that we already have so I'm going to use this big angle here that's my angle in the middle my C uh it's X we already worked out from the previous question 5.40 we know 19 from the question itself and because we worked out this angle notice these questions leave into we actually know that this angle here the whole angle is going to be 90 plus the answer we just worked out 38 dot dot dot which is going to be equal to 110. 38 dot dot dot so let's bring all this together for our formula so the area of the triangle I'm just going to write down to the examiner that I know what it is half a sin C and let's just pop in all the numbers that we have so a half times well we know what x was that was the 5.3 96 dot dot dot we know that the B side would be 19 so * 19 and then times the sign of the angle in between so that's 110. 38 dot dot dot notice with this kind of question they are usually quite lenient in if the answer is not exactly accurate they'll still give you all two marks let's try and make it though as accurate as possible so we have zero oops there we go so 0.5 times uh 5396 probably should be using a few more decimal places but we'll use this for the moment 19 times and we want to use S [Music] here of 90 plus answer because the answer from before was that smallest angle that we had so I'm try to use that just to minimize any rounding errors so I think we' got everything there and then we get to our final answer of 48.5 2 48052 and that rounds then to 48.1 so let's just check the mark scheme make sure that's accurate enough for the mark scheme yes it is you see actually it should be between these two numbers so both 48.0 or 48.1 is correct but the best thing to do is try and keep as many decimals in the question as possible just so you don't miss on any accuracy marks at the end notice with the MK scheme here they give you a range to get it between so 48.0 4 and 48.12.1 so again try and keep those questions as accurate as possible right on to our next question so question five so the area of the triangle a b c is 34.1 square cm now as soon as I see this I know that formula we looked at in the very last question half AB sin C is going to be useful in some way we're given AB is 12.4 angle ABC is 30 and now we need to show that BC is equal to 11 so we're looking for this side here so what I'm going to do is just use that area formula that we have so area is equal to 12 a b sin C and now let's just put in what we know well these are the two sides A and B and this is the angle in between so C so if we substitute this in well 34.1 that's our area of the triangle is equal to our half time well a is 12.4 B we don't know that's what we're looking for here so I'm just call this x that's the side we're looking for times the S of the angle in between sin 30 now I could simplify this down because sin 30 is a half and you can find half 12.4 but what I'm going to do here is just let the calculator do this for me I want to get the X on its own so I need to divide by a half * 12.4 * sin 30 basically I want all that on the other side of the equation soide by a half * 12.4 * sin 30 if I do this well these all cancel that leaves me just with X and then I get 34.1 ided a half * 12.4 * sin3 and now I'm going to let the calculator do the donkey work here and work out exactly what this is so we type this in so 30 4.1 ided 0.5 * 12.4 times the sign always very satisfying when you put this in and you get the exact answer you're looking for here which is 11 so we just going to pop that in and that's equal to 11 cm guaranteeing that one Mark excellent now we're going to move on and work out AC so let's have a look here I now know this is equal to 11 cm and I want to work out this length here let's just call that y so I look at the triangle I have here I've got two sides I've got the angle in between I'm looking for the side opposite this calls for the cosine rule now remember the cosine rule was c^2 is equal to a s + b^ 2 - 2 a COS C and now I can just substitute everything that I know into this so we're looking for this side so y^2 is equal to well a s and b^ 2 so 12.4 2 + 11 2 - 2 * 12.4 * 11 * the cosine of the angle in between which is 30 and remember I want to find y on its own so what's the opposite of squaring well I do need to square root on both both sides so notice I haven't reached my calculator yet I'm waiting until I get to this final step so Y is equal to the square < TK of 12.4 2 + 11 2 minus Open brackets 2 * 12.4 * 11 * cos 30 and you can pick up a lot of marks on these questions by just knowing these formula and working through these questions nice and carefully and logically so let's pop this into the calculator and see what we get so we're going to start with a big square root it's going to be a big square root by the end so 12.4 squar + 11^ squar minus this is where brackets are really really important so please do include them 2 * 12.4 * 11 * the cosine of the angle in between okay hopefully that's all enough brackets there so always double checks so checking my working here on the left hand side checking that with what I've just typed in I press my enter button and I get my answer of 6 21 okay so it's pop that across so uh 55 dot dot dot now usually I would write this working here in this space for B if we round this then we're just going to get 6.21 CM so and always check your rounding for these kind of questions as well don't to put units twice to get my answer of 6.21 and now we're looking for angle cab remember that middle letter tells us where the angle is so we're looking for c a b using the letters that are given in the question so we're looking for this angle here as soon as I look at this I go well I've got a side and an angle and angle and now I know this side because we just worked this out this was uh 6.2 055 dot dot dot so this calls for using the sign rule so when you've got a side an angle and side and looking for another angle then we're going to use the sign Rule now it's all about labeling here so let's do a different color so you can see what we're doing in this particular question so I'm going to call this big a I'm going to call this now small a I'm going to call this Big B I'm going to call that small B right let's do it on this slide here so we're going to go sin a over a is equal to sin B over B so a we don't know the side opposite is 11 so we get sin a over 11 is equal to S of B which is 30 / by that side we literally just worked out so that's 62055 dot dot dot again we want to get the sign on its own so what's the opposite of dividing by 11 what we need to Times by 11 on both sides we do that then we get sin a is equal to 11 sin 30 over that 62055 we're not quite done before we use the calculator what's the opposite of signing something or inverse sign on both sides this gives us then a is equal to sin inverse and then everything in that fraction so 11 sin3 over 62055 dot dot dot remind me to try and use as many decimal places as possible let's go and see what the calculator says so we start with trick sign inverse first open up our fraction so we have 11 Time s 30 close brackets and now I can use the answer from the previous question so I can go control answer that will then take this answer here that I've just used let's make sure there's brackets there and then we get our answer of 62.4 13 62. 413 and that rounds then to 62.4 De you check the mark scheme again that falls within that range that we've looked at here that's absolutely fine notice I do try and keep it unrounded when I can because it does give you the most accurate answer in case there are any problems with the accuracy there at all and my last question is to find the length of the perpendicular line from a to the line b c so this is a slightly different kind of question here so let's go back to my diagram so imagine I drop a perpendicular line from B on from a to the line BC so from a to the line BC so this is what they mean imagine this is perpendicular now as soon as you see that word perpendicular you know that there are right angles there so perpendicular diagr is getting a bit messy now basically mean means they meet at a right angle okay so what I like to tend to do in these kind of questions is separate the problem just so I can see what's going on so what I'm going to do is draw this triangle at the top here with the information that I know so I'm going to rotate it round okay so that's my right angle here I don't know this length this is what I'm looking for I know the hypotenuse CU it's opposite the right angle is 12.4 and I know that this angle here is 30 which is over here so I just done a quick 2D representation of exactly triangle I'm looking for here and once we know that then we can simply use sakaa our classic so let's get labeling those sides um don't know why I put a degree sign there there we are so this is going to be opposite cuz it's opposite the angle this is the longest side and this time we are not going to use tan like we've done before CU you've got O So of SOA which one's o that's going to be the so so if we draw our formula triangle we have sin Theta * H and O so we need to know these formally triangles like literally off by heart we are looking for the opposite so we're going to do s of the Ang angle * H so our answer for X is going to be sin3 * 12.4 and you'll see that is 6.2 now how do I know that 6.2 without using the calculator because I know my exact values so I know sin 30 is equal to a half so it's just a half * 12.4 which is just equal to 6.2 no rushing to my calculator for that particular question again I really do recommend if you need to know those exact values then do check out the link just as you see above because that goes through exactly how to work out sin 30 sin 45 cos 60 tan 45 and so on so here's the mark scheme again you can have a look and see what I've done and where I've picked up all the method marks for these particular questions okay and on to question three so it's going to be a little bit more on the easier side here so on diagram BC CD is a straight line again important because we've seen that in previous questions and the first thing we need to do here is work out the length of a c so notice we've got a right angle triangle so Sakura should be in your mind the first thing we're going to do is label those sides so this side I've just done in Black here is the hypotenuse this here is the opposite the angle and now I think SOA so o is of course in the so category just like the previous question nice follow on from what we just did so H and O this time we're looking for the h so cross out this and we're going to do this calculation on our calculator the opposite divide by side of the angle so AC is equal to 30 ided by sin 37 this time it's not an exact value so let's use that calculator so we're going to talk type in 30 divided by S 37 close brackets and we get 49. 849 849 dot dot dot and that rounds to 49.8 M three marks is pretty generous but again towards the start of the paper you want to make sure you've got those fundamentals there secure right on to Part B so we're now looking for the side BC let's have a look side BC okay so this side here well we can use the same triangle that we did before y just checking we're doing BC here so this time this is the adjacent side um now you could use opposite or hypotenuse at this point because we know both I tend to use the value that I already know from the question so this time we've got OA the OA so we're going to use in this case the TOA the tan so we have tan Theta * a over there and this time we are looking for the adjacent side so we don't want the adjacent so we're going to do opposite divided by tan of the angle so BC is equal to opposite is 30 divid by tan of the angle so tan 37 again let's go to that calculator so almost identical process to what we did before here so you get 30 divided by tan this time so tan 37 and then we get our answer 39.8 39.8 so we just pop that in interesting that question I mean we can just use course tan we could have used um cosine as well if we wanted to that seems the most straightforward method and now we need to work out the side CD so CD is this side here let's use a different color so the way I would approach this because we've already know this side because we just worked that out this was 39.8 dot dot dot which will come back to what I'm going to do is work out the length of this entire side going all the way along and now I can use basically the same calculation because this is now my big adjacent side so I'm going to do exactly the same calculation as before so to work out BD I'm going to use 30 / tan 26 and do that on the calculator data and then I can just take BC away from BD to work out CD just to show you my working here CD is going to be BD minus BC to then find the final answer so let's get the calculator involved now so I'm going to do a nice little trick here I'm going to store the answer is a so every time I type in a I've got that 39.8 ready for the next question now I'm going to work out what I just typed in there so 30 over 10 26 so 30 over 10 26 gives me a bigger side and then I can just do answer minus a and then that will give me my direct answer here so let me just write in these things so 30 over 20 26 that's 61.5 is dot dot dot dot and then my final answer being 2.69 dot dot dot dot dot which then goes to 21.7 M like so so not I use the functionality of the store function just to help me avoid any rounding errors whatsoever and now for question D they want to work out the area of the triangle ACD so they want to work at the area of okay the smaller triangle so that's worth highlighting here so in this case they want the area of this triangle so as soon as you see area of triangle need to be thinking ah I want something to do with half AB sin C and what you want to do here is see if you can use any sides that you've already worked out well we worked out CD just here this is a bit bright yellow let's use a different color so CD was equal to that 21.6 n that we did uh that side here so that hypotenuse that was from part A that was the 49849 dot dot dot and we know the angle in between angle on a straight line again got a straight line here add up to 180° so this is going to be equal to 143° and now we can use everything we just talked about to work this out so the area of the triangle is equal to a half times well these two sides that 49849 dot dot dot times literally what we just worked out so 21. 69 dot dot dot times the S of the angle in between which was 143 just showing my working now I haven't used Too Many decimal places here so let's see if we get the exact answer they're looking for so we're going to do 0 0.5 times uh [Music] 49849 times the answer we just did times the S trick s 143 that gives us 325.7 perfect dot dot dot dot and then that gives us then to three significant figures 325 exactly popping that answer in there right so you can have a look at the Mark scheme so you can see any answer between 325 and 327 is valid there and all the method marks that we picked up going through that question if you look at that question you've got 3 69 11 11 marks so in terms of the actual paper that's probably about 8 % of your paper just by doing this particular question here and this is one of the best ways to improve on igcc questions by topic really just today we're just practicing trigonometry getting really really good at it seeing lots of different styles of question and it really does help with your general understanding of this topic right and let's move on to question nine so diagram here shows triangle a c and now we need to use the cosine rule to find angle ABC now the bad thing about the formula sheets compared to other courses is they only give you the one for a side so c² = A2 + b^2 minus 2ab B cos C which is not very useful when you're actually looking for an angle what I'd recommend is actually to learn the angle formula off by heart for your exam now the angle formula is a rearrangement of this now I'm not going to go into this in detail on this video but we can rearrange this formula to give us this instead so a s + b^ 2 minus c^2 all divided by 2 a I recommend you learn this off by heart then we have less pressure in the exam in having to rearrange a formula Under Pressure so please do learn this once you know this this is simply a case of substituting into the formula now we're looking for angle a b c so we're actually looking for this angle here so if I label it with the letters I've got here this would be Big C this would be small C and then these two sides doesn't matter which way around are going to be a and b once we know that we can just substitute into the formula so cosine C is equal to a s + b 2 so 8 2 + 6 2 minus c^ 2 which is 12 2 divided two lots of a b so 2 * 8 * 6 here we're actually looking for the angle so what's the opposite of cosigning something well inverse cosine on both sides if we do that this cancels always good and so we get the inverse cosine of 8 2 + 6^ 2 - 12 2 over 2 * 8 * 6 and this is where the calculator comes in we're going to pop it all in so we're going to go to uh trig and inverse cosine let's set up my fraction once you do you know a good you know 45 minutes of these kind of questions you start getting really comfortable where the functions are and you feel better as well I've actually thinking you've really understood the topic very very well so 8 squ + 6 s - 12 2 2 * 8 * 6 on the bottom enter and then we get our answer of 117.8 7 11727 if we round that then Jon again round to 3 SF I'd round that to 117° to three significant figures it's quite nice in this question because they tell you what rule you need to use in order to work out the calculation and the next one is also similar we're going to use the sign rule here to work out angle b a c so remember the sign rule sin a over a equal sin B over B so if we go back to this now in order to use this we need to have an angle so what I'm going to do is just go to my calculator now and store this the way I'd store it remember I go to control and store I'm going to store it as B so every time I type in B I get that particular angle so there's no rounding error okay and once I've done that let's just now label this up with a different color so you can see what's going on here so we're looking for b a c so we're looking for this angle here b a c and notice that we're going to make this our big a so the side opposite the six is going to be our small a and then this here is going to be our Big B Because is the angle that we do know and the side opposite the angle we know we're going to call small B and now we just substitute this into the formula so we get sin a over 6 exactly equals s of 11 7.27 what we just worked out divided by the side opposite which is 12 and you're probably used to this at this point we're going to rearrange to make a the subject so what's the opposite dividing by six timesing by six on both sides sides giving us sin a is equal to 6 lots of sin 11727 dot dot dot divided by 12 and now we want to get the angle so what's the opposite of signing inverse sign on both sides this cancels this which is very very helpful and now we're going to find sin inverse of that horrible fraction again using that stored value that we used before very very useful function particularly for questions like this so let's again pop this into our calculator so we're going to have inverse sign control and divide and we're going to type in six not equal sign don't want the equal sign I want a sign there we are now B remember was our uh symbol that we're using to store that particular angle at the top here and then 12 at the bottom we press enter and we get to our answer 2638 to 26.385897 interesting they've wanted this to one decimal place which is interesting usually it's three significant figures so okay one thing I would highlight then is that they want all angles to one decimal place generally I would think three significant figures is absolutely fine and I to be fair I did show the 0.27 in the working of the question as well right uh if you want more practice with these questions you see I've gone through about a half PowerPoint I've prepared today so if you want practice by yourself and see if you really understood the concepts that we've talked about well you'll see there are more PowerPoint uh questions here so you can really check your understanding the link for that is in the description below so you can go through this at your leisure and really get that practice in that you need to in order to really understand what's going on okay so hopefully you found this useful this tutorial I think this is quite a good way of doing it I've gone through questions here for a good amount of time to really check your understanding and now it's your turn to go go off uh take this PowerPoint go through the solutions I've done to the first part of this PowerPoint and now really try and extend your knowledge here by practicing the questions you'll find in the PowerPoint in the description below and if you want practice on SS then do click on the video you see in front of you