Pythagorus' Theorum - Math Lesson 3,4,5 triangle - By tecmath
Transcript
00:0-1 | Welcome to the Tech Math channel . What we could | |
00:02 | be having to look at in this video is we're | |
00:03 | going to be having a look at how to work | |
00:06 | out that unknown sides on a right angle triangle . | |
00:09 | Like using this really , really great little our theory | |
00:13 | . It was discovered by this guy about 2.5 1000 | |
00:15 | years ago . You know , ancient Greece ? This | |
00:17 | guy called Pythagoras . In fact , it was that | |
00:19 | cool theory . And they named it after . This | |
00:20 | is called Pythagoras theorem . So Basically , the fear | |
00:25 | of a pythagoras is this , it says for any | |
00:27 | right angle triangle , this is a triangle that has | |
00:30 | a 90° angle here . We often put a little | |
00:32 | square little thing down there to show that it's 90° | |
00:36 | , but says that in a right angle , try | |
00:38 | the longest side . We're gonna call here . The | |
00:41 | high pot news can be worked out . Okay , | |
00:43 | so first I'll write this great word off . Hi | |
00:49 | , what did you use ? Okay , I'll start | |
00:52 | all this again . So for any right angle triangle | |
00:54 | , the longest side is known as this high point | |
00:57 | is the theory of pythagoras . States that you can | |
01:00 | add the squares of the lengths of these two shorter | |
01:03 | sides here . So you get the square of this | |
01:05 | side , of the square of this side , and | |
01:08 | if you add them together they're going to be equal | |
01:09 | to the square of the hypotheses . Okay , Did | |
01:13 | you get that there ? So the way that they | |
01:16 | write this is is this they have given these guys | |
01:19 | letters and you probably might have uh you may or | |
01:21 | may not . This may be the first time you've | |
01:22 | heard of these , they call the shorter sides A | |
01:26 | and be . And this high potency is E . | |
01:29 | S . C . And it leads this really really | |
01:32 | , really often used formula in bats , which is | |
01:35 | this one that I squared ? He saw it here | |
01:40 | . The number squared plus b squared this side here | |
01:46 | squared equals see squid . Okay , this one here | |
01:51 | , that's for a right angle triangle . And this | |
01:54 | is a really , really great thing to be using | |
01:57 | . You can use this in carpentry when you're trying | |
01:59 | to square up things to make walls going at a | |
02:01 | 90° angle . So it's a really , really great | |
02:04 | little method of working out unknown diagonals , unknown sides | |
02:09 | , squaring up things that you want to be 90° | |
02:12 | here . Okay , so it's a great little thing | |
02:13 | to be able to use . So let's use this | |
02:17 | theory , this theory right now . Okay , You've | |
02:22 | given examples like this one . Okay , so we | |
02:24 | have here , we have a couple of shorter sides | |
02:29 | here . We're gonna work off just these shorter sides | |
02:31 | to work out this longest side to start off with | |
02:33 | . And I'll make another video where we can do | |
02:35 | the other ones where we work off to work these | |
02:37 | shorter sides out . So , so for instance , | |
02:39 | we wanted to work out the length of this longer | |
02:42 | side from here , through to here . The way | |
02:46 | we can do this is using pythagoras theorem . Okay | |
02:49 | , So I squared plus B squared . So I | |
02:53 | want to get back to this is a really important | |
02:55 | triangle . This one in particular , because C squared | |
02:58 | , we know it's a right angle triangle , it's | |
02:59 | going to be here and I wouldn't put it in | |
03:01 | there . It wasn't okay , because we're also going | |
03:03 | to look at how we can deal with triangles that | |
03:04 | are not right angle triangle . You know some other | |
03:07 | videos , how we can work out under and size | |
03:09 | on those . So first off , it doesn't matter | |
03:13 | which one you call A or B . As long | |
03:14 | as you recognize that A . And B . And | |
03:16 | the two shortest sides . So Let's call this one | |
03:19 | a . And this one be so a squared is | |
03:23 | three squared plus B squared , which is four squared | |
03:28 | equals C squared . Okay . Three squared is died | |
03:36 | plus four squared four times four which is 16 . | |
03:40 | And this is equal to C squared . Yeah , | |
03:43 | I'm running out spaces . So I'm gonna say this | |
03:45 | also equals nine past 16 . What does that equal | |
03:48 | ? This is equal to 25 . Okay , so | |
03:54 | c squared equals 25 . This means that C . | |
03:59 | Siegel's 25 . We can work out see while working | |
04:03 | at the square root of 25 . Okay . What | |
04:07 | number ? Three times by itself to get 25 ? | |
04:10 | And the answer to this is five because five times | |
04:14 | five is 25 . So long aside here is five | |
04:18 | centimeters and this is such an important little triangle . | |
04:21 | This this is known as . Okay , so we | |
04:24 | got a three and a 4 to 5 and often | |
04:27 | what I'm teaching , a bunch of carpentry guys who | |
04:29 | I teach , I often really stressed the importance of | |
04:32 | this one because you don't necessarily have to have a | |
04:34 | squared b squared c squared all the time when you're | |
04:36 | squaring up walls . But the major thing that you | |
04:39 | can do is if you want to actually get a | |
04:41 | wall coming out at 90 degrees Because you can use | |
04:44 | this idea of it . 345 triangle . Okay , | |
04:48 | we actually call this a 345 triangle . Okay . | |
04:56 | And it can be worked out using pythagoras is there | |
04:58 | ? But if you can do this and you have | |
05:00 | your tape measures , you can work this out and | |
05:02 | you can measure from here to here is three m | |
05:04 | . And this wall that you want to say , | |
05:06 | the way I'd usually do is I get this would | |
05:08 | be the wall I've been putting in and I Put | |
05:11 | a three m coming out was there ? And I | |
05:12 | have a from this point here also five minutes and | |
05:15 | where they meet up should be 90°. . So it's | |
05:17 | a great little way of actually also working at 90° | |
05:20 | from a point . Okay . Let's have a look | |
05:22 | at another example here to say we had this particular | |
05:25 | example . How do we work at this high pot | |
05:28 | news here at the right angle triangle where we can | |
05:31 | use this , A squared plus B squared equals C | |
05:36 | squared . Okay , so I squared I'm going to | |
05:41 | call a this time . This one down here . | |
05:43 | Okay , why not ? Okay , so this is | |
05:46 | not swear plus Basically , which is two squared equals | |
05:51 | c squared . Okay , nine squared 9 , nine | |
05:55 | . Uh I d would plus four squared the two | |
06:01 | squared , which is all is going to be C | |
06:04 | squared which is equal to 81 plus four which is | |
06:08 | 85 . Okay , so what we could do is | |
06:11 | we could actually call this uh we could work out | |
06:14 | this is a search and that sort of deal , | |
06:16 | which I've looked at another videos as well . But | |
06:18 | for this I'm just going to actually come out with | |
06:20 | a fairly rough answer using a calculator . Okay , | |
06:25 | so if we were to get 85 , we can | |
06:29 | work out the square root of this by going in | |
06:33 | verse X squared . So it's 9.219 So we're just | |
06:39 | gonna cause 9.2 . So this is equal to 9.2 | |
06:46 | . I probably should be saying that C . is | |
06:49 | equal to the square root of 85 to c . | |
06:52 | is equal to 9.2 centimetres . She's I hope I | |
06:57 | put my units up there . I didn't It's really | |
07:00 | bad . Okay , this is celebrators . Okay . | |
07:03 | It was a big price . Why didn't put that | |
07:05 | in there ? Okay . Really important to put the | |
07:07 | units in there ? I said I always forget as | |
07:08 | well . Okay , let's have a look at another | |
07:12 | example to say we had here . 12 centimeters and | |
07:17 | seven centimetres . Again . The same formula I squared | |
07:22 | plus B squared equals C squared . All right , | |
07:30 | let's substitute in some values here . So let's call | |
07:33 | a square 12 here . Okay ? So 12 squared | |
07:37 | plus B squared , seven squared equals C squared . | |
07:42 | Okay , so 12 12 , 144 plus seven squared | |
07:51 | +77 of 49 this equals C squared , Which is | |
07:56 | equal to 49 Plus 144 is 193 . Okay . | |
08:06 | 193 . That means C is going to be equal | |
08:10 | to the square root Of 193 . And that off | |
08:14 | the top of my head . I don't know . | |
08:16 | I'll be honest . So I'm gonna go 193 inverse | |
08:21 | square . Oh I think I got the wrong one | |
08:24 | there . Let's type that in again . 193 In | |
08:28 | verse Square is 13.8 died . Okay . 13 point | |
08:35 | I thought uh benefit unit tonight . Senate meetings . | |
08:40 | Okay . So how did you go with this ? | |
08:44 | Um now the next video I'm going to be putting | |
08:47 | up here is going to be looking at how we | |
08:48 | can work out these unknown side . So yeah , | |
08:50 | we're gonna look at how we can work out uh | |
08:53 | if the triangle is not quite 90° what we can | |
08:56 | do that ? Okay . So hopefully I'll see you | |
08:59 | then . See you next time . Bye . |
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