3,4,5 rule - Free Educational videos for Students in K-12

3,4,5 rule - By tecmath

Transcript


00:00	Good day . Welcome to Tech Math channel . What
00:02	we're gonna be having a look at in this video
00:04	is 345 triangles , which uses some ideas from pythagoras
00:07	theorem . This is a really handy little thing to
00:09	know for things like building , mainly when you want
00:11	to put in walls , things like this , you
00:14	want them to come out at angles 90 degrees ,
00:16	Really nice and square . So I'll start out by
00:18	drawing a 345 triangle . So this is a 345
00:22	triangle . You're going to see it's a triangle that
00:24	has a side length of three units , a side
00:26	length of four units and a side length of five
00:29	minutes along the side here . Also between the two
00:32	shorter sides of three and the four units sides ,
00:34	we have a 90 degree angle and this is the
00:37	part that makes it really handy for squaring up a
00:40	building and making a wall come out exactly 90 degrees
00:43	. So how would you go about using one of
00:45	these ? Well , if I wanted to actually make
00:47	a wall that came out exactly 90 degrees , I
00:50	would do the following . So at the moment you
00:52	have this existing wall which would be occurring along here
00:56	. Okay , so from the particular point where you
00:59	wanted this wall could come out 90° , you would
01:03	measure four units up . So whether that before feet
01:07	or four m , depending on where you are ,
01:09	you would measure this four units up to this particular
01:12	point here and you might put a little math there
01:14	or a nail or something like that from this particular
01:17	point . Now , where you actually wanted your wall
01:20	to come out from ? So this is the existing
01:21	wall . You want a wall to come out from
01:23	here , You could measure three units , okay ,
01:27	and that's a long hair And you'd roughly try to
01:31	do it around about 90°. . And out here you'd
01:34	have your three metre mark . Okay ? Now ,
01:37	at the point where this hit exactly 90° where this
01:40	was exactly 90°. . The point between this part here
01:45	where you've measured four m in this part here ,
01:48	Where the three m comes out should be exactly five
01:51	m . And so you'd have to stuff around a
01:53	little bit and maybe move this back and forth .
01:57	But as you did that , you would eventually hit
01:59	a point with this where the distance between this became
02:04	five m . And when you did this , you
02:07	would be exactly 90 degrees . And that's how 345
02:11	triangle works . And we'll help you actually are put
02:13	in a 90 degree wall . So what's going on
02:16	here ? Well , for any right angle triangle ,
02:19	the side lengths can be worked out using Pythagoras theorem
02:23	, and I'll show you how this works . Pythagoras
02:25	theorem states the following that a squared plus B squared
02:29	is equal to c squared . What does that mean
02:32	? Well , A and B . Are the two
02:35	shorter sides . And it's basically saying if you square
02:37	one of the shorter sides and add it to the
02:39	square , the other shorter side , well , the
02:41	result will be the same as the square of the
02:44	diagonal here . So let's try that out . We'll
02:46	put a here , we'll put be here , we'll
02:49	put see here . All right . So let's give
02:51	it a go . All right . Uh , So
02:54	I hear is for so four squared plus B squared
02:58	, which is three squared should be equal to five
03:01	squared if Pythagoras theorem is working , and you know
03:04	, it's going to write otherwise , I wouldn Catalonia
03:06	. So four squared means four times +44 times four
03:10	is 16 . 3 squared is three times +33 times
03:13	three is equal to nine , and this is equal
03:15	to five squared five squared five times five is 25
03:19	so 16 plus nine is equal to 25 that's true
03:22	. 16 plus nine is 25 . Pythagoras theorem is
03:25	proven on this particular . Are +345 triangle here .
03:29	Okay , So why is this so important ? We'll
03:32	just pretend that you were doing this on a bigger
03:36	building . Okay . To see why this is so
03:37	important is a lot easier on a bigger sort of
03:40	room . Yes . So we had a 10 m
03:42	by 10 m room that we're putting on . We
03:43	have this wall and we want to come out 90
03:45	degrees and make everything good and square . So We
03:49	have 10 m here and we can actually square up
03:51	using a 345 triangle . Okay , so once again
03:55	, what we could do is we would have four
03:56	m here and we would measure out three m and
04:00	we would end up with This side here . That
04:03	should be five m . Okay , so this should
04:05	be 34 and five , and this year should be
04:09	90°. . But say we were a little bit inaccurate
04:12	and we didn't actually do are squaring up as good
04:16	as we could , and instead of actually making this
04:18	90°, , we made it 89° were one degree out
04:23	. How much do you think ? Actually , this
04:24	would throw you Over the course of 10 m ?
04:27	It would actually obviously , yeah , the it was
04:31	slowly , slowly , slowly , slowly , slowly ,
04:33	slowly , slowly come out a bit . But how
04:36	much would it come out ? And you may be
04:38	surprised with this , but I've worked it out a
04:40	little bit earlier that the actual difference that you would
04:43	actually get from that particular error . If you didn't
04:46	89 degrees and didn't square up properly would be around
04:50	about 17.5 centimeters , 174 mil to be more precise
04:56	. Okay , So it's a really important thing that
04:59	you do to go through and actually get these right
05:01	. This is a huge difference , right ? Uh
05:04	Not only will it cost you a heap of money
05:05	if you do this , but it's also going to
05:07	provide you endless aggravation as flaws don't look right and
05:11	walls don't fit properly and tiles maybe don't go very
05:14	well . Look , you know what , it's just
05:16	really good that you would go through and make sure
05:19	this is 90° and get it exactly . Okay ,
05:22	so it's important to spend the time and do that
05:25	. So anyway , um , how could you go
05:27	about and even make that a little bit better ?
05:31	So if we wanted to square up this 10 by
05:32	10 m room , what we could actually do to
05:34	make it even more exact and not go out that
05:37	particular amount here would be we could use pythagoras theory
05:41	and once again , we know that a squared plus
05:43	B squared is equal to C squared , R two
05:47	shorter sides A and B . Because we want this
05:50	90° angle here , the diagonal is going to be
05:55	just here . This is going to be C .
05:58	So we could work out what that particular sizes .
06:01	Okay , So what would it be ? All right
06:03	. So , we have uh I which is 10
06:07	10 squared plus B squared , which is also 10
06:10	squared is equal to c squared . We don't know
06:13	what that is yet . All right . 10 square
06:15	10 times 10 is 100 plus 10 by 10 ,
06:19	which is 100 is equal to c squared . So
06:22	, what the c squared equal or c squared is
06:24	equal to 100 plus 100 100 plus 100 is 200
06:29	to see is going to equal the square root of
06:33	200 . The square root of 200 is 14.142 m
06:39	, which is equal to 14,142 millimeters . You can
06:44	supplement a similar sort of thing if you are using
06:47	feet and inches there . So this particular site here
06:52	, if this is 10 and this is 10 would
06:54	be 14.142 m . Okay . And you can actually
06:59	get out your tape measure , you can measure up
07:01	10 there , you can measure at 10 there and
07:03	when it's 90 degrees exactly who they are , You
07:06	should be 14 m , mm or 14,142 mm .
07:14	So for more practice in these , I'll put up
07:16	a link to questions already have on pythagoras theorem .
07:19	It's a really , really handy thing if you're working
07:21	in the construction industry or even if you're doing something
07:23	like this at home , I've used it myself .
07:25	Okay . It's a great way of squaring up and
07:28	I'll tell you The maths that you do here will
07:30	save you so much anger later . If you don't
07:34	do it , you do not want to be out
07:36	90°. . Okay . Uh , anyway , so that
07:39	link will go up there if you like the video
07:41	, please remember , like and subscribe to the tech
07:43	mouth channel . Thanks for watching . We'll see you
07:46	next time . Bye .

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