Pythagorus' Theorum - Math Lesson 3,4,5 triangle - Free Educational videos for Students in K-12

Pythagorus' Theorum - Math Lesson 3,4,5 triangle - By tecmath

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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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