GCSE MATHS: Bearings Exam Practice LIVE LESSON 12 EDITED

hey guys just before we get into the lesson I just want to let you know that you can catch these Live on YouTube uh every Tuesday from 6 p.m until 7 P.M in the UK time and that means you can be more interactive you can ask your questions and they'll be answered okay so without further Ado let's get into the lesson so welcome back to another one of the GCSE tuition lessons so again we're doing bearings today so if we just get started now um again this first question is pretty basic in terms of bearings but a few things we need to remember whenever we're talking about bearings is they are always measured clockwise from the North Line okay so from North Line and the other thing to remember is that they're always three digits Okay the reason for that is it's a bit of a nautical things when you're talking over the radio if you know that every single angle is three digits if you've missed a number you can then ask them to repeat it so again it's not really relevant in maths but it is relevant when you're using bearings in the real world so that's two of the main things however the third thing which is where I think some students do get kind of confused on is so first of all is the three digits so I always see students drop a mark because of three digits but the second thing is kind of reading this so it says write down the bearing of B from P so the way I like to do I like to think of it is where it says from p that's where we're looking from so we're starting at p and then we're going to B okay so of B from p means we start at p and go to B and it says write down the bearing so again it's just the angle from the north line so in this case it's just 120 degrees so again hopefully that's not not too bad but again if you're not sure again stop me because when we get on to the later questions they involve things like the cosine rule and everything so it can get a bit more tricky and the next one says work out the bearing of a from P so once again we're starting at p and we're ending up at a okay so if I just delete these two actually just this bit careful just delete that Circle there what I'm looking for is again I start at the North line from p and I'm going all the way around until a okay so that's the key thing to remember there and this isn't actually too tricky to work out if we look at it it's basically a full circle but 90 degrees taken away so we're doing is we're doing 360. subtract 90 which is 270 degrees okay so far I think that's not too bad um I think with the next question it's actually involves measuring so I'm going to talk through this one because obviously I can't measure it on the screen I don't think I have it protractor with that one but actually let me just check do I no yeah I didn't think so so uh you can also be asked to measure bearings so just really be be aware that you're supposed to put the protractor the zero line should be along the north line and then you're just measuring that angle there okay so again so a lot of this is to do with kind of scale drawings and I think I may have made a slight error here because a lot of these are scale drawings that should be fine so a lot of these are scale drawings and is there anything that you guys want me to go through with scale uh just one thing to note is that they'll generally give you a scale of like one centimeter equals one meter or something and then you're also able to measure like using a protractor or a ruler okay so assuming that that's all okay with scale we can go down to this next one uh scale's not okay do you mean so one of the ones that we can kind of do is this one isn't actually a scale drawing so the only time you can assume that it's an Acura or a or you can actually measure the values is if it literally says um oh it is okay yeah is if it literally says that the diagrams drawn accurately if it doesn't say that then you cannot measure using a ruler or protractor even if it looks like it so you have to look for the word accurate so for this one it says Oxford is on a bearing of 330 degrees from Cambridge so let's just write uh say Cambridge is here see now we're going to draw our North Line now what we would do is we'd measure an angle of actually you know what I need to move this over slightly towards the middle now 330 degrees again it doesn't say that I that it's accurate so I don't need to use a protractor but if I know that you know all the way around 330 degrees I know that 360 degrees is going to sorry 330 degrees would be something like this okay okay so again the full circle will be 360. this is about 270 so slightly bigger will be 300 degrees okay again it doesn't need to be accurate it's a key thing to remember and this is a North Line so again from Cambridge means we start at Cambridge and then we've drawn basically a massive reflex angle of 330 degrees okay oh it's got the zero one sec okay so far is that okay again just stop me if I stop making sense now we're looking for the bearing of Cambridge from Oxford so if we have a look that is going to be this angle here okay now I want you to keep in mind that bearings is going to use most predominantly it's going to use the angle rules we have this Z angles and co-interior angles normally so if you want to get really good at bearings you always want to think about um Ultra angle theorem so that's the Z angles and you want to think about co-interia now if you think about why this is all northlines are parallel so if I have a look at this angle here and this angle here they are co-interior angles because the two North lines are parallel okay which means they add to 180 and I think this is where a lot of students get confused because alternate angles can be used in almost every single bearings question and we're going to I'm going to show you some examples of that in a minute but this one is co-interia okay now this angle here is 30 degrees right because the full circle is 360. we've taken up 330 so 360 minus 330 is 30 degrees so to work out this bearing we just use co-interior angles so the bearing of Cambridge from Oxford is just 180 minus 30. so remember with co-interior angles they add up to 180 degrees okay so even though my diagram that does not look like 150 degrees it's fine it's not accurate it's not accurate drawing is that okay I would recommend in every single question making sure you draw the diagram okay just draw a nice little sketch so you can see what's going on okay because the next one's going to be slightly different even though it looks like it would be the same so if we start here the bearing of London from Liverpool so I guess I'm gonna have to label both of them in this case which is a shame so this is going to be Liverpool and London is 130 degrees so if we say this is the North Line 90 degrees will be going straight across like that so it needs to be slightly bigger than that so let's say something like this that's going to be my London again doesn't need to be accurate and then again you have the North Line now the bearing of London from Liverpool is 130 degrees so if we go clockwise from North that'll be so as you can see it's not this exact same as this question it's slightly different so finding the bearing of Liverpool from London is going to be clockwise from North so it's going to be this reflex angle now again co-interior angles this angle here will be 50 degrees because those two angles need to add up to 180 because the north lines are parallel so it's like a c angle so this reflex angle here while angles around a point add up to 360 so it's just going to be 360 minus 50. equals 310 degrees and if you have a look at my diagram it looks a bit like 310 right it's bigger than three quarters of a circle so again drawing a diagram is the you can't just copy the method you need to know the the diagram to draw I'm actually probably going to need to find more questions for this because I didn't realize that a lot of them was scale questions so I'll look through some more exam papers but we have two exam questions now so this might interest you a little bit more because this is where we're going to get into the big stuff but so far we all okay I think a few people have left so yeah okay perfect okay so now uh the first question is an ed Excel question we have an AQA one coming up in a second but they're actually very very similar they're almost identical and we have something that looks like this this is the most recent bearings question from an actual Edexcel paper except for the 2022 papers because I couldn't use those because we use them for mocks in the school I teach at have a look okay so this is where things get a little bit more tricky so we have a bunch of distances a bunch of bearings that's all okay find the bearing of Charlton from Acton so if we start from actin here right we want to essentially find this whole angle here right so we start acting the bearing to Charlton okay this gets a bit funky so there's a few things that we can try and figure out um I don't know this angle inside the triangle right and I don't know this length so ideally I'd like to work one of them out now it's not a right angle triangle and I can't make it one okay because it's not isosceles either at least I don't know if it's isosceles so I know I'm going to be using the sine or the cosine rule but I don't know which one yet however this is where things can get a bit tricky and this is a trick that you can use for almost every bearings question if I continue this North line down okay this little angle here is going to be 30 degrees because angles on a straight line add to 180. okay now this angle is actually an alternate angle because these two North lines are parallel can you see it's a big Z if you trace this it's on its sides you might have to tilt your head a bit but that's a big Z angle so this angle here 37 degrees is that okay so I'll leave that for a second there's two halves to that all good perfect Lila you okay with that cool now I'm going to delete this because if you actually look at the Mark scheme they don't give credit for finding two separate angles they only give credit if you know to add them to get 67 degrees okay okay let's think have you got any more information we've got some more information what can we get now again I want this angle inside the triangle here right that's what I'm aiming for to find the bearing but at the moment I don't have enough information to do it but what do I have enough information to work out well okay let me put it this way if I want to find this angle here right I'm going to need another angle side pair because I want to use the sign rule because I know what the opposite side is and I have this angle so I want to find out this side here if that doesn't make sense let's think of it another way what can I work out well this is actually a perfect scenario for the cosine rule right because I have two sides and the angle between them and I want to work out the third angle um you can also use a corresponding angle yeah I actually know this isn't a corresponding angle not quite because this line here we can't say is parallel yeah so what we're going to use is we're going to call this a and we're going to say that a squared equals B squared plus c squared minus 2pc so then a is just equal to actually a square is equal to B squared it doesn't actually matter which way around we do this 9 squared oh sorry cos a it's got the most important part of the cosine a nine I've seen your message I'm just going to read it this is called the cosine rule if it helps they give this one to you in the exam but in my opinion knowing how to use it is far more important so let's get our calculators out I should have mine still open for my last lesson cool so then we just sub this in so we have lost 8 squared Plus 9 squared minus two hey tap on the keyboard's a lot harder than using the calculator in real life seven and then we're going to describe the answer because I don't actually care about the four values let's call it 9.42 yeah just to make sure it's as accurate as possible cool I'm hoping you can see that because I have an angle and its opposite side and I have one other side I can use the sine rule to find out this inside angle here right so that won't give me that it will give me this so if we want to label it up let's call that a this a this B and this B right it doesn't actually matter what we call it so we have sine B the angle we want over the opposite side nine equals sine 67 over 9.42 so remember with the sine rule you can flip it if you want so do the sides on top over the angles or you can do the angles over the sides it's the same thing so in other words we have sine B equals 9 sine 67 over 9.42 and then from there we can work out what the angle so again that's probably a bit trickier of a question but uh we're not actually done yet so I shouldn't jump the gun sign 67 close bracket over 9.42 then don't forget this gives us what sine B is to find B we need to do the inverse sine of our answer 61.6 degrees let's call it uh yep so now the actual bearing is 61.6 plus 37 which would give us 98.6 degrees so we should keep in mind that we need to give it as three digits so this would actually drop your mark so you would say oh nine eight point six so again from here to here you can actually drop a mark which is a bit of a shame and that's a five mark question um quite a few steps I'm not gonna lie but how is that in terms of how you're feeling good lighter how's that for you the next question is going to be a um AQA question but I want you to have a look you need someone's cosign rule I have done a video on it a few weeks back um so you you can have a look when to use it is a good question so when do you use the cosine rule so if you have a triangle that doesn't have a right angle in it that's cosine rule and sine Rule now Wendy is the cosine or the sine rule well the cosine rule you use when you have two sides and the angle between them quadratic formula yeah sure that's fine if you want to find a question I'm more than happy to go through it or I can find one that's okay or do you mean quadratic formula with the cosine rule that can also come up yeah uh here's the AQA question again if you look it looks almost identical to the nxl one so okay no just chill perfect um so I would like to just take a second is um bearings doesn't come up all that often so it's easy to run out of questions but look at other examples because the method and the tricks are all the same okay so you can practice that way except it's fewer marks uh this one's paper two the Edexcel was paper three um so yeah so we have to work out the direct distance from P to R so the reason why this is four marks is there's one fewer steps so what we're basically looking at is this distance here and as you can see it's not a right angle triangle so we have a few bearings and we need to work out the third side okay so let's think I need to work out the third side of a non-white angle triangle so I'd like to use the sonal cosine rule but I can't however again it's the same trick as the last question right if we draw this North line coming down that now becomes angles on a straight line add to 180 so that must be 25 degrees and again these are alternate angles so this angle here is the exact same as this angle here so that's also 80 degrees so in total that'll be 105 degrees to process that and this is actually a lot faster because all we now need to do is work out what a was in the Ed Excel question except this is the AQA question so again we're going to use the cosine rule why are we using the cosine rule we have two sides and the angle between them and we want the op the third side Okay so we can call that a if we like so then we have a squared equals I'll write out the formula again let's get to it um doesn't matter which way around we call it so 12 squared plus 28 squared minus 2 12. 28 cos 105. and then we just write what a is and we're done so once again you're gonna have to deal with how slowly I type this because I'm not used to typing on a keyboard on a calculator 28 squared minus 2 12. 28 that wasn't too bad cause 105 and remember we need to square root this answer which is why it's so hideously large we get 33 it doesn't actually give us how many decimal places so three significant figures make sense to me uh 33.2 miles which another thing to look at when you're checking answers is if this third side was a lot bigger than the other two like again when we had a thousand miles we know something's wrong but uh yeah so unfortunately I didn't prepare this as well as I thought I did because I expected the other questions to take us longer and I didn't realize how many scale factor questions we have so I'm going to find some other bearings questions quickly so if you bear with me and again if you know where any can be um I know I really thought I prepared this better I didn't realize how many scale factor questions there were which is really annoying that paper a paper ah cool oh never mind that's the paper that's the paper I just did great yeah bear bearings doesn't actually come up as much as you'd think um which is so you're right so I actually did try and use these online protractors before but they're they're very wonky um so like importing something in there and then obviously the scale's off then you know which is kind of annoying I'm assuming you guys know how to use protractors um I can do a lesson on that but wow berries really didn't come up at all Circle equations um so it's in like equations of a circle uh that is 100 uh planned coming up so with Ed Excel I've actually gone through all of the recent papers and it doesn't look like there's any any bearings at all really well no bearings really that's really strange it was yeah it was in 2022 so oh yeah Lila that's a common mistake um it was in 2022 you're right but unfortunately since schools use them for mocks uh even I don't have access to them even though I'm a teacher and what we can do is actually go to the old spec as well so I know that some people don't like old spec but okay my maths hasn't changed in thousands of years so ah finally okay this is a decent question this is an Edexcel question um but I will find an AQA question after this sorry that's taken me so long but I'll cut it out in the edited version it's fine um one uh page 12. okay ah current page wait where did that it printed underneath this why why did it do that I think my curse was that's why I printed underneath you can't have 3D bearings no I've never seen that anyway I've never seen 3D bearings that would be interesting though wouldn't it you can't it's you wouldn't be able to describe a bearing in three dimensions you'd need to have two angles how far up and down how far left and right so if you want to go like really far into further maths and stuff you do have um two sets of angles to describe position and things like that but yeah you 99 9 UM so yeah although technically this is old spec if you look the question is very similar to what you'll be doing anyway and then I'll do a I'll do one from the comments back anyways let's go to it so Manchester Airport is on a bearing of 330 degrees from a London Airport find the bearing of the London Airport from Manchester again fairly simple if we say Manchester would be let's say over here 330 degrees would be an angle about there we have London so if we look at our two bearings North I may have made a mistake there so from London to Manchester will be clockwise 330 degrees and we want to find the bearing of the London from Manchester so we're looking for this bearing here if you look we've done a very similar question this angle here would have to be 30 degrees and then because they're co-interia they need to add up to 180 so this would be 150 degrees so that's our answer again without drawing a diagram I'd find that tricky myself the London Airport is 200 miles from the land okay that's nothing to do with bearings at all never mind I thought that was thousand airports 200 miles from Manchester Airport playing these Manchester Airport at the flight to London one I mean that's not too tricky you're just doing distance over time right so 200 over 120. um I'm assuming you guys are okay with that let's find another one yeah it doesn't seem like Eric summer has many bearing questions which is interesting so I got the 2021 paper so let's go through the Higher One if there's something else you want me to go through please let me know because I feel like I'm wasting your time a bit here again I do want to apologize for the uh after lesson that you're doing at the moment um if you want something else that's completely fine um but I think bearings was one of those tricky topics right so if you'd like to stick to that I'm glad for that Lila but I'm not gonna lie this one is very uh this one's not good I really thought the other questions weren't scale but I didn't read them properly so you know I didn't listen to my own advice and uh read the question yeah kind of ironic I suppose but I'm glad you find them useful and yeah just uh let me know if there is anything else you want to do well is there really no other bearings okay I've gone through every AQA past paper and I can't find any more bearings questions actually there's a one marker look at the bearing of C from a okay uh Evie with that you would make it plus but I would recommend using brackets and you don't even have to think about it okay so if you have a negative B term um yeah so if you have a negative B term I would very much recommend just using brackets so let's say you had like 2x squared minus 3x plus 4. I'm actually not sure if this is solvable then when you're writing your quadratic formula which is you do minus and then minus three so it would become positive but this way you don't actually have to think about it and I don't like to think um this one is possible no it isn't never mind yeah this question actually isn't possible you get no Solutions yeah so I always use brackets because then I don't have to think about stuff like that um yeah I can't believe it we've done every single bearings question really there's only been three I actually really thought there's more than that [Music] um I mean I could look at OCR but so have I but I think that they were just found online so they may have been from like previous spec questions you know what I'm being stupid GCSE bearings questions classic right now that's scale I don't want to do scale I want to do actual hard exam questions those are bad Match Made Easy baby I don't know about this where's the worksheet uh if it's on YouTube um is there any you want me to go through or do they just go through them anyway if they go through them anyways I don't know if there's much point in me going through it as well um again I'm trying to make sure that this is worth your time okay let's just download something oh cool I can do that yeah I can absolutely do that uh I've actually found some questions but I'm not going to lie they're very similar to what we've done okay I have found some of them aren't great but some of them are four I'm really hoping it prints in the right place this time so I don't have to hey not bad Okay so there we are get some more so we can do some of these there we are it's fine only wasted 10 minutes it's fine 10-15 minutes so with the alternate angles and everything uh I can't do a recap of those and it might be quite useful to do before we go on so what we have is when we have parallel lines um okay how it's best to do it imagine these lines are straight and they're parallel you have a few different types of angles that can be made so for example if I draw a line between these two okay because the lines are parallel these two angles will be the same and that's called some people call it Z angles because if you trace it kind of looks like a z and that's called the alternate angle and these are always equal to each other if I draw another set of parallel lines I can also have like an a line going from here to here these two angles so if we call them A and B in fact let's let's make this a bit more clear so in this case a is equal to B in this case it's called co-interior angles okay uh the other way you might hear them called is C angles but I would like to stress you cannot call them z f or C angles you have to call them by their proper name okay and this is just that a plus b is equal to 180 degrees so far not too bad um if I were to draw another set of two parallel lines again just imagine these as straight and I draw a line going down here these two angles are equal and this is called corresponding angles and again you may hear this called f angles because it makes like an F shape and that's just a equals B that's pretty much all you need to know um there are some others like vertically opposite angles so if you have two lines like this the opposite angles so if we call these a b c d all of the opposite angles so A and C are equal and that should be it yeah that's a really brief summary of them I think to be honest the trick of it isn't remembering them the trick of it is applying them uh so let's do some bearings and see if we can work it out so again you can see that where they've gotten from these are all old spec questions but perfect Lila so these are all old spec questions in the new spec it's come up literally once in AQA and once in Edexcel uh except for the 2022 papers as you mentioned Evie uh 2022 AQA had one as well let's not quite rare so positions of a yacht ship S and A B can be by the way these come back in a level math so it's good to know the bearing of B from y okay so of B from y would be we're going 2B from y so it'd be this massive reflex angle is 228 degrees okay so again if you disagree please let me know and the bearing of s from Y is 118 degrees so just this part here is 118 degrees okay so this looks hideous okay so I'm going to kind of shorten this a bit 228 minus 118 would give me 110 degrees so what I'm going to say instead if I get rid of this is that this angle is 118 and this angle is a hundred and ten I'm going to stop there for a second just to make sure that that's all okay any questions about that at all again that's just to make my diagram look a bit nicer and oh I answered the question so if we draw a line go from here to here they want the angle b y s uh I'm done it's 110. so it is just 110 degrees not bad so yeah using bearings with trig so this is a right angle so we can think we're just using sine cos tan and Pythagoras not too bad diagram shows the positions of Two Towns A and B and oh this isn't bad at all is it actually this could trick people this could definitely trick people citizens 110 and 60 right so work out the bearing of B from a okay now my immediate reaction was just work out what x is and we're done but keep in mind the bearing of B from a would also include this top bit here okay so it's not just X it's also X plus whatever this little bit is here so so just be extra careful but we do need to start by working out X okay so if we label our and our sides this is the opposite side that's our hypotenuse and this is our adjacent so if I just get rid of those dashed lines to make me feel better we have the adjacent and hypotenuse and we want our angle so if we write out sohcahtoa adjacent and hypothesis means we're using cos so in this case cos x is equal to adjacent which is 60 over 110 so then X is equal to the inverse cos 60 over 110. I keep thinking about press escape to just never mind so 60 over 110 close bracket 56.9 degrees also for those of you you should keep in mind because you have a non-calculator paper certain values of sine cos and 10 you need to remember unsure of that there is a bit of a trick I can show you uh to remember that oh whoops that's not the answer okay jumped ahead a bit so the question is we have the little inner bit how do we work up the filter oh you learned them nice one there is a little counting trick you can do which I thought was really cool but uh I'll show you that maybe a bit later just memorized okay so it's not the hand one this one blew my mind okay I'm just gonna take a detour because uh this was really interesting so the values of sign you need to remember if I remember correctly is 0 30. do you need to have 45 as well yeah you do okay good uh 45 60 and 90. yeah perfect now with sine right you might already know that it goes you know assign X will go if you imagine this is like a table right it that's not really given me much room okay it goes zero and then it goes root two over two sorry it goes um one over two then root two over two and then so on right so you can actually um remember this so against root two over two then root three over two and then two over two which is one right here's a really cool trick all you do is you count using square roots so you have square root zero over two square root one over two square root 2 over 2 square root 3 over 2. square root 4 over 2. oh you have seen that okay this blew my mind on us all right but yeah so you're just counting and then with cos x you go backwards right so cos 90 would be zero over two cos 60. so root 4 over 2 is just going to be the same as 2 over 2 which is the same as one so you're literally just counting counting up if that's what you mean Lila I'm not sure if I made a mistake there and with cause you just do it backwards so cos zero is one sixty is root yeah my tangents intersect um if you have the equation of tangents you can equate them okay if this is a circle theorem question don't forget that the lengths of both tangents is the same so it makes a giant isosceles triangle but if you have an example question we can do that okay but let's quickly go through this to work out this little bit up here all we need to do is work out this angle and if you look we're using the ultimate segment theorem in alternate segment alternate angle theorem in Reverse so this angle here is just going to be 180 minus 90 minus 56.9 because angles in a triangle add up to 180. um kind of Eevee all you need to do is equate the two expressions so it's basically simultaneous equations you're right so if I go 180 we get 33.1 so if this angle is 33.1 it means this part here is 33.1 so the total bearing is going to be 33.1 Plus 56.9 and that will give us our value which is 90 degrees now again keep in mind we can't give bearings as two digit numbers such as zero nine zero uh does that make sense I did kind of there's not much space so I haven't done it super clearly is this too easy or do you want to jump to harder ones they do get a bit harder so let's keep going uh but some of them do get a bit harder I want you to know um but we can how long do we have 15 minutes question five yeah cool so let's have a look using angle nausea call um the bearing of B from a62 yeah work out the bearing of C from a so basically we just need to work out this angle here right okay okay again if I have a look at this if I follow this this is a big Z angle right so this x angle even though it doesn't look like it is also 62 degrees Now with an isosceles triangle base angles are always equal so this angle here and this angle here are equal to each other so all we need to do to work those out is 180 minus 62 which would give me 118 then half that give me 99 degrees what am I talking about 99 degrees 59 degrees is what I meant to say okay so this is 59 degrees so the total bearing is all the way from North all the way around so it's just going to be 62 plus 59. uh if you disagree with me please let me know again I don't actually have the answers to these questions so actually the answer is probably at the bottom 121 degrees and because it's three digits all done yeah so the answer is actually 151. they're 21. uh is that okay again maybe you're finding it a bit easy I can jump up ahead good all right um tradition of a being a lighthouse score oh they don't give us the bearings okay ship a is five kilometers from L on a bearing centuries from l so this here is 70 degrees again as I'm labeling this uh try and check to see if you would label it the same if not let me know because again I could be wrong you know it's possible it's happened and B is three kilometers from L on a bearing of 210. so basically this total angle here is 210 degrees okay so the easier way to write that is if we do 210 minus 70 that's 140 so what I can do instead to make this look a bit neater is right that this angle here is 140. okay I think you can see what we need to do here right calculate the distance between ship A and B so in the chat what we're going to do again you'd have to work it out just uh say what we're going to use or why or whatever here we are perfect so again cosine rule so uh I'll go through it anyway might as well a squared equals two sides with an angle in the middle perfect exactly so again what we label B and C doesn't matter because we're just adding them and timing them and if you know adding and timesing are both commutative which means it doesn't matter which order you do them in doesn't matter which order I add or times two numbers in it does if I subtract and divide not five times five because on the 40. and we're done not too shabby yeah it does seem like in the new spec they don't really use them that often uh bearings which is interesting I remember it coming up a lot when I did gcses about 10 years ago um but apparently not So Much Anymore which is interesting and then square root answer 7.55 because it tells me three significant figures right 7.55 not too shabby also I do have a small announcement at the end of The Lesson by the way which is slightly unrelated to this but uh oh okay this is actually really important in a level maths as well so it tells me here abnc are three villages B is 6.4 kilometers due east of a so what would the bearing be of B from a so what would this angle be here if something's due east this will come up a lot in a level maths especially mechanics which is why students hate mechanics of why that what that would be oh fair enough not bad okay some students don't know that 90 degrees is 100 correct because north east south and west are all perpendicular to each other well done yeah you apparently are geniuses Genie I perfect um everything else is fine I think so that means this angle in here is going to be 210 minus 90 which is 120 degrees right and we need to calculate the bearing of B from C so if I draw a line up here we want this angle here interesting this is a pretty hard question not bad um let's have a sink okay this one might be a bit tricky wait did I get the angle right of B from C that's correct okay this one's caught me off guard a bit not gonna lie let's have a look so the first thing is I need this interior part of the angle right um which again uh we actually did a question like this the Ed Excel question we're going to use the cosine rule followed by the sine rule okay so let's do that cosine rule to work out this side again you guys know it I'm not gonna uh force you to keep repeating yourself because let's just do a equals yeah because uh again feel free to have a go by yourselves because you might get the answer before I do I hope not whoops whoops whoops making mistakes minus two four zero point eight because 120 okay this is an interesting question then I'm going to square up my answer yeah 8.93 okay so we know that's 8.93 kilometers and then if you remember how we worked out this kind of inner angle before we use the sine rule because we have an angle and its opposite side we have another side so we're going to work work off the angle is so I'm going to call it sine C because it's the angle at C over 6.4 because that's the side opposite it is equal to sine 120 over 8.93 so sine C equals 6.4 sine 120. over 8.93 between C equals let's have a look see so bear in mind when I say I have the answer I literally just have the numerical answer and I actually don't have any proof that it's correct so this should be an interesting experience and an investite answer 38.4 degrees okay okay cool cool cool cool cool okay I've got it so this next part is going to be a bit interesting so because I can't really work out a way to work out this so we've worked out C we want to work out what I call it X which is that little angle up there so again if we think about our angle rules this line is parallel to this line so if I know what this angle is I can use co-interior angles exactly easy so that shouldn't be too tricky that's just going to be 360 minus 90 minus 120 so it's basically 360 minus 210 which of course is 150 degrees and then if you remember rightly co-interior angles have to add up to 180 so 180 minus 150 equals 30 degrees okay so again co-interia uh and then all we need to do is add them together right so one other thing about bearings is technically you should not write them with a decimal place ever okay so I know there was a question earlier that said give to three uh was it to one decimal place that kind of threw me off because normally they say bearings need to be to the whole number so my advice um always round it to the nearest whole number unless you're specifically told to give it to a decimal place and yeah here are the answers so 68 was correct not bad I think that went pretty well besides the time when I ran out of questions and spent 15 minutes for physics three sig figs do three sig figs um unless told otherwise um Technically when if you do a level physics you'll know that it's not really that it's just the lowest number of sig figs in the question but yeah three sig figs I'll do okay two really but what if it's like a number like 364. so I mean you have to give it to 360. so okay Evie that might have been in an experiment so the only reason why I can think that would be used for is when you're doing the voltage experiments um because the ammeters read to one decimal place always but other than that two Sig fig I wouldn't say that's that's that's the case at all no yeah so the exam question might have been about an experiment if not then that's not right definitely not I mean that that's that's fine like writing 5.0 instead is fine but if you do two Sig fig always then you do this which doesn't make sense and to be honest I haven't really seen anyone graded down for that 5.05 but like I went round to yeah that doesn't make sense if you want you can look through your mark scheme um for whatever examples you're doing and you can double check but I've never heard of that ever um anyways so to the announcement so I don't know if you guys look into the in the description of the videos but I do actually choose a pupils um I have in-person classes and they're in Hounslow if you've never heard of Hounslow then don't worry about it because you won't be close enough but yeah I do them in a school in Hounslow the school I teach at which I'm not going to announce online obviously for hopefully obvious reasons but I do uh in-person tuition I also have started online tuition classes so if you're interested in that and it's for maths science and a levels then feel free to email me my email is in the description of every video I make but just in case you're interested it would be that the reason why I'm announcing it is because I really want to fill up the classes so I can help as many people as possible but that's the email of course I'm still going to do these free YouTube sessions obviously um that's gonna be fine but I do a level and GCSE maths and also GCSE Science and a level physics specifically um but it's in person and online um again never heard of Hounslow just completely forget what I just said but I do online ones as well if you're interested but I'm not like a shill I'm going to keep doing these uh free YouTube sessions but uh let's just so you guys know okay uh