Pythagorus' Theorum - Math Problems - Free Educational videos for Students in K-12

Pythagorus' Theorum - Math Problems - By tecmath

Transcript


00:0-1	Good day , Welcome to Tech Mouth Channel . Uh
00:02	, we'll be having a look at this video is
00:04	going to be looking about how to find . We're
00:06	gonna be using pythagoras theory once again , and this
00:10	is pythagoras theorem here , which states that basically ,
00:14	if you square the sum of the two shorter sides
00:17	on a right angle triangle square , this side on
00:19	this side , you add them together , it's going
00:22	to be equal to the square of the high point
00:24	news . This long side here . Okay , so
00:26	we've been using this previous videos using this , A
00:29	squared plus B squared equals c squared idea . Okay
00:33	, so what are we using this in this video
00:36	to work out the side length to say some of
00:40	the unknown uh , sides were , I'll give you
00:43	some examples here . So , we're gonna be having
00:45	a look at where we're gonna be . You might
00:47	get asked to solve a problem that requires Pythagoras theorem
00:50	, where there's no right angle triangles , and how
00:52	we can actually use Pythagoras theorem to work out different
00:55	things like this . So , for example , you
00:57	might get is this sort of thing . We are
00:59	asked to work here . The unknown side here .
01:03	This is not a triangle , but you got a
01:06	couple of right angles here . Okay . And we
01:08	want to know what this particular length here is .
01:10	We can use this pythagoras theorem , A squared plus
01:13	B squared equals c squared , and a bit of
01:15	logical deduction to work out unknown . Solidly . Okay
01:20	, the way we do this is as follows .
01:22	So what you might realize first off is wicked ,
01:25	draw a line down here . Let's go draw it
01:27	as a dash line . If I was to do
01:30	that , I'd end up with a little triangle down
01:32	here that had a right angle here . Okay ,
01:36	So we actually do have a right angle try here
01:38	. I want to find this one here , but
01:40	we actually do have a right angle trying we can
01:42	make because this side length here is going to be
01:44	10 this side the theater which is the other one
01:48	we need . Well if this site here is 12
01:51	and this one here is 15 , it means that
01:54	If here to here is 12 or so , which
01:56	it is . That means this one here must be
01:59	three . Okay , so we can use pythagoras .
02:02	Is there ? So I squared plus B squared the
02:08	fools C square . Yeah . Um So what let's
02:15	substitute in some values here . Okay , so let's
02:19	call this side here . I This is 10 squared
02:24	plus B which is three square and this is equal
02:29	to this long side here . X squid . Okay
02:37	, Let's work out 10 squared . It's 100 plus
02:42	three squared which has died and this is equal to
02:47	X square . So X word is equal to 100
02:53	Plus nine is equal to 100 the door . Okay
02:57	? So what we can do is we could square
03:00	root both of these are gonna end up with x
03:02	and X is going to be equal to the square
03:04	root Of 109 . So the square root of 109
03:09	, if you have worked this out , I'll get
03:10	it calculated to do this . I don't know that
03:12	off the top of my head . So 109 in
03:15	verse squared Is 10.44 . So this is equal to
03:23	10 avoid for so really the trick with this is
03:29	try to spot the right angle triangles that you can
03:32	possibly make to help you solve these types of questions
03:36	. Okay , so really setting it up is the
03:38	key with this sort of thing . So I'll give
03:40	you another example here . This one here . What
03:44	we want to know is we want to know not
03:46	only this length here , but we also want to
03:48	know this length here . Okay , so this is
03:52	basically we're gonna be using Pythagoras theorem to work out
03:57	one triangle and then we're going to use that side
04:00	leaf here to work out the length . Sorry ,
04:03	the high park news of this triangle . They were
04:05	going to use this number here to work out this
04:07	high park news of this triangle . Okay . Do
04:10	you see ? Okay , so let's do this first
04:14	particular triangle . Call this triangle one and I'll call
04:17	this triangle to so we're going to work out the
04:20	high pot news of triangle 1 1st . Okay ,
04:25	so let's do this . We have So for Triangle
04:30	one , I squared must be squared equals C squared
04:38	. Hey there , what have we got here ?
04:40	So a squared is 10 square plus B squared is
04:46	eight squared equals six . Quit . Okay . Yeah
04:54	. 10 squared is 100 Plus eight square which is
04:59	64 equals see squid , which is equal 264 .
05:07	Okay . So what you might realize is that C
05:10	squared is equal or C is going to be equal
05:17	to the square root Of 164 . Yeah , I'm
05:21	just gonna horse for a minute and say this is
05:24	actually not a bad thing to leave that for a
05:26	minute . You're going to see this in a second
05:28	. Okay . Ah This idea . Okay , I'm
05:32	going to get back to this in a second .
05:33	Singles 160 for when we're working at this next triangle
05:37	. Okay , But I can work this out on
05:40	a calculator . So let's go 160 for in verse
05:45	Squared equals 12 . so equals 12 for you hide
05:53	. Okay , so that's X . X . is
05:55	equal to 12.8 . So how did you go with
05:58	that ? That's part of our answer . Let's get
06:01	the next partner . So we know this part here
06:03	is 12.8 . So once again , we're going to
06:05	use a squared , B squared , C squared .
06:07	Ok , So when you use ice squared plus B
06:11	squared equals C squared at this time for tribal to
06:17	Yeah , just a little trickier . I was going
06:19	to get to this but say we call this a
06:21	squared here . Yeah . We already know that .
06:24	This number squared . Which is this one ? This
06:27	number squared . Is this one ? So I can
06:28	write the standards . 164 Yeah . Plus B squared
06:36	. Which is four squared equals spokeswoman's Y squared is
06:41	the so 164 plus 16 vehicles , Y squared .
06:52	And they moved out of it , I reckon .
06:54	So why squared ? We add these guys together and
06:58	we're going to get 164 plus 16 is 180 and
07:05	this is what Y squared is equal to . So
07:09	why equals the square root 180 , which is equal
07:14	to 180 uh , inverse square 13.4 . Okay ,
07:25	So we have two answers . We have this one
07:28	here , where why is equal to 34 ? And
07:32	we have that X . Is that good at 12
07:34	for that ? Okay , So there are two answers
07:37	for that particular question . Let's go to one last
07:40	example . This is a bit more of a common
07:42	example . Say you have to work at the height
07:45	of this particular triangle here . Okay . Maybe you
07:48	want to work at the area of it and say
07:49	it's work that out . You would have to work
07:51	out the high because we need to base into high
07:53	. So let's look at the formula for pythagoras ,
07:56	which is A squared plus B squared equals C squared
08:03	. And we've got this height here that we want
08:04	to work out , how are we going to do
08:06	that ? So let's go to caution you with this
08:10	. Uh , what we have is we have a
08:15	squared . If I was to make a triangle out
08:17	of this , I'll just draw , draw this over
08:20	the top of this trial we have here . We
08:21	have heart here , which is the thing we're trying
08:25	to work out or call that X . Okay ,
08:28	I didn't make that overly clear . I've got to
08:29	write an excellent . But this is what I was
08:31	meaning for us to work out , was this unknown
08:34	height here ? So what we're going to do is
08:38	this is going to be X squared and this is
08:43	going to be attitude B squared . Okay . The
08:48	squares not 10 , is it ? It's half of
08:49	them . Okay , So it's five squared and this
08:54	is equal to C squared , Which is 10 square
09:01	. Okay . Just drawing on these things occasionally makes
09:04	them a lot easier to deal with . You know
09:06	, if you have a textbook might make it a
09:08	bit hard . Right ? Okay . So let's work
09:10	this out . X squared plus five squared is 25
09:16	equals tense word . What ? Okay , what are
09:21	we left with ? X squared ? And before I
09:26	go that far , let's do this . Let's get
09:31	x squared by itself . So to do that ,
09:33	what do we have to do ? We have to
09:34	take 25 off both sides ? And what we end
09:41	up with ? Is this okay ? Because we want
09:42	to get this X squared by itself ? Okay ,
09:45	So we're gonna end up with X . Word And
09:50	these two are going to cancel each other out .
09:51	100 take away . 25 and 75 . So X
09:55	. Is going to be equal to the square root
09:58	75 . Which is equal to let's get a calculator
10:03	at the old trusty calculator 75 in verse . That
10:07	is 8.66 . Okay , so right 0.66 Centim .
10:17	So the height of our triangle here is 8.66 cm
10:22	. Hey look , you could use this now to
10:23	work out the area that because you can go half
10:25	base times height , is that it would be like
10:27	43 or something like that . So it's pretty cool
10:31	. Yeah , it does have its uses anyway .
10:33	I hope that was of some help . Ah Anyway
10:37	, I'm gonna leave you with that . Okay .
10:39	See you . Bye .

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