Sin Cos Tan - Basic Trigonometry - Working out unknown sides - Free Educational videos for Students in K-12

Sin Cos Tan - Basic Trigonometry - Working out unknown sides - By tecmath

Transcript


00:0-1	Good day and welcome to the Tech Math channel .
00:02	Uh , what we're gonna be having a look at
00:03	this video is we're looking at using trigonometry . We're
00:06	looking at in the last video , um using this
00:09	trigonometry to solve for unknown sides . Okay , working
00:13	on the inside , So first off , uh ,
00:17	let's just give a quick recap what we have to
00:19	look at . Last video , we have to look
00:20	at . First off had a name of different sides
00:23	of a true economic triangle , like a right angle
00:26	triangle . When we're using trigonometry , we have a
00:29	couple of different names for different sides . So we
00:31	had this angle here . We call that theater .
00:33	We have the long side here which we call the
00:35	high pot news . We have the side opposite theater
00:39	which was called the opposite and we had the adjacent
00:43	side here which was called Jason . Okay , so
00:46	H O . And I . And then we had
00:49	these true economic functions . Okay , the economic functions
00:53	you're going to see here , we have . I'll
00:57	just put the calculator up here . This is a
00:59	calculator on your computer . By the way . If
01:00	you don't says this particular one , you want to
01:03	see it more like this . You can hit view
01:05	and go to scientific . And if you do this
01:08	, you'll notice that these three buttons here , we
01:09	have signed cars and tan and a lot of scientific
01:13	calculators have these as well . We're gonna be using
01:15	these three trigonometry functions . Sine cosine tangent . And
01:19	so the functions are as follows . We had soy
01:24	because the 10 . Okay . So it because 10
01:31	And these functions , these ratios are as follows the
01:36	way I remember it was this , I remember this
01:38	little new monarch called some old hags . Can't always
01:41	hack their old age . All right , son .
01:43	Old pegs code . Always hack there . Old age
01:53	. Okay . So we have if we if we
01:58	have theatre with the sides , we're gonna be playing
02:00	around with the opposite and high pot news , we're
02:02	gonna be using sign . Alternatively , we might be
02:05	having theater and we might be using the adjacent high
02:07	pot news . In that case we use a co
02:10	sign or if we're using theater and these opposite and
02:14	adjacent sides , we're gonna use tan . Okay .
02:16	So we're gonna be using these to sell some unknown
02:19	sides right now . So , first off , I'm
02:23	gonna put a list of rules . I reckon the
02:24	Youtube that we are going to follow when we solve
02:27	these . Okay . First off , we're gonna three
02:29	are particular problems going to label the sides . Well
02:31	then work at the trigger gnomic function which one of
02:34	these particular ones here we're doing ? And then what
02:38	we'll do , we'll substitute values in and then solve
02:41	our equations . So let's do this right now to
02:44	say we had this particular problem here . It's a
02:47	nice looking problem . It's a beautiful problem . It
02:50	looks a lot like this . Okay , so it's
02:52	a triangle . It's a right angle triangle . The
02:55	little writer du bois here there . Okay . And
03:01	what we have is we have theater here , which
03:05	is going to be let's call it 30 degrees .
03:11	We know the side here , which is right .
03:17	And I wish to know the opposite side here ,
03:21	which are gonna call X . Okay , So how
03:24	do we solve this ? First off , we have
03:28	to label our scientific case of this when you do
03:31	these really follow these steps through . So it's really
03:34	important that you know how to do each part .
03:37	So first off , you should be able to label
03:39	the sides . We have theatre , we have the
03:41	long side which is called the high part . In
03:43	years , we have the opposite side of theater called
03:46	the opposite . And we have this adjacent site .
03:50	So which particular ones that we're using ? We're using
03:53	the opposite of the high pot news . So you
03:56	might remember we had some so first off of label
04:01	decides and we're now will hit the tree atomic function
04:04	. So some old hives because always uh huh .
04:12	There old age . Okay . Which one are we
04:19	gonna be using ? Well , as you see ,
04:23	we're dealing with the opposite of the high point news
04:26	. So this is the side here . So we're
04:28	gonna be using side . So we're right that a
04:31	bit nicer than this . Okay , let's write this
04:33	out properly . So the rule we're gonna be using
04:37	is soil equals opposite over some old hags opposite over
04:46	white hot news . Okay , so The way that
04:50	we actually write this now is we write sign and
04:53	the sign of what sign you say . It's a
04:56	sign of 30°. . So 30° is a thing we're
04:59	going to be using side with and it's equal to
05:03	the opposite , which is X Over the high pot
05:08	use right before we do anything . Let's get X
05:13	all by itself . So what can we do to
05:14	do this ? Well , at the moment , this
05:17	side is divided by eight . So if we just
05:19	multiply this side by side , we're gonna get rid
05:20	of . So we also have to multiply this side
05:22	by eight . Okay , another way occasionally want to
05:25	do this just to chuck another random little thing in
05:28	and it's a really handy whenever you get stuck on
05:31	these is this , I actually write this equation down
05:35	here at three equals six over to Article six ,
05:41	divided by this means this number equals this number divided
05:45	by this number . And it's true . Yeah .
05:47	It's also the same sort of format as this here
05:49	. We're trying to find out this number up here
05:52	where the X . Is . So what would we
05:54	do if it was this 60 ? We're trying to
05:57	find out we would multiply this set up so we're
05:59	gonna multiply these two numbers . Okay . That's just
06:04	a little trick I use . Okay so to work
06:07	at X We're going to multiply signed 30 topside .
06:16	So let's do this . You might have a scientific
06:18	calculator but I'm going to use this calculator here .
06:21	Okay . So it's it's on the scientific mode .
06:24	So let's do this and type in 30 we had
06:27	side Which is .5 times right equals four . Okay
06:37	. So answer his ex equals four . Okay .
06:43	How did you go with that ? That's a nice
06:45	easy one to start off with . Okay . All
06:48	right let's let's go through another example here . So
06:51	yeah that's that's our answer . Let's go through another
06:54	example and I'm not just gonna make it so it's
06:56	necessarily going to be the next one is going to
06:58	be a cause one of the next one then after
07:00	will be a tam one . I think it would
07:02	be too easy . Okay , So I'll try to
07:06	be fairly random with . Okay . Oh yeah ,
07:10	Okay . Yellow . The other triangle . It's fairly
07:11	random as well . What about we do this ?
07:13	I do uh this line here and it's actually a
07:19	little bit bigger so we can see what's going on
07:24	. Okay , let's put some sidelights on this .
07:29	So , first off , yes , this is 90°
07:31	. uh let's make theater here . Uh Let's make
07:36	it 66 degrees . Okay . And I'm going to
07:43	we're going to try and work out whose side X
07:46	. And we know that this site here is 15
07:50	. How's that sound ? All right . That's a
07:52	good little random one . So first off , let's
07:54	label the sides here . So we have the long
07:58	side here is the high pollen . Is that's the
08:00	one . We're not going to use a We're gonna
08:03	have The opposite to our angle here . This is
08:06	the opposite and with the other one which is running
08:09	alongside and the adjacent . So we've labeled our sides
08:12	. Now , we have to work at the trigonometry
08:13	functions . So some old eggs could always hack they're
08:23	old page . Which what are we dealing with ?
08:28	We're dealing with the one that's not the high pot
08:30	news . So it's not this one not this one
08:33	. It's 10 . Okay , so let's write this
08:35	air nicely there . Okay . Sorry , we'll get
08:41	rid of those . And we have here we go
08:46	. We're going to have 10 equals there old .
08:53	I tend 66 degrees Equals the opposite , which is
09:00	15 . However the adjacent which is X . Okay
09:07	, so I'm gonna do that similar sort of thing
09:08	again . Where what I did was I wrote uh
09:12	you know because this one there you get exports by
09:14	multiplying over here . We have to export self that
09:17	, don't we ? So what I'm gonna do with
09:19	this , Is that gonna rewrite this thing up here
09:22	? So three Equals six divided by two . Okay
09:27	, so we were trying to find the one down
09:29	here is too valuable . Okay , this one here
09:34	, so what we were doing to get this too
09:35	is we go this one divided by this one ?
09:39	Okay so this one divided by this one this one
09:42	divided by this one this one divided by this one
09:45	. Okay , so x equals this 1 . 15
09:50	divided by 10 66 degrees . Okay let's do this
09:58	calculator . Uh clear . And we'll go 15 divided
10:08	by 66 . 10 equals 6.67 . Okay . 6.67
10:22	. So How did you go with that 1 ?
10:25	Pretty good . Okay if you've got 100% sure when
10:29	you're doing this may be what you wanna do is
10:31	you want to go 66 10 you might want to
10:34	put that into the memory . So memory class And
10:38	then you can go 15 divided by memory . Read
10:41	equals 6.67 . In fact I should be rounding that
10:45	up to 6.68 . It's gonna be more correct .
10:50	6.6 sites . Okay should I go with that one
10:55	? Let's just do one last example . Hopefully .
10:57	Yeah . Okay I'll make it because one you know
11:00	I'm going to do it . Well I suspect I'm
11:05	gonna do a cosmo . Maybe I'll be a little
11:06	bit tricky and we'll make it something that's not close
11:09	. That's how I look . It doesn't really matter
11:11	, does it ? Okay . So what about we
11:13	do one last one here and we do this .
11:16	Here's my triangle and it's a nice good lofty sort
11:20	of triangle . Big long sort of triangle . I
11:22	mean , and this is what he is going to
11:24	be . Um , I'm going to call this one
11:27	here . What about we call this 1 ? are
11:32	going to be doing , uh , in fact ,
11:36	we're gonna do , let's make it , cause what
11:38	, how would I do that ? Let's work in
11:40	with that . We're going to go . Can't always
11:43	had a bit of a reverse engineering , isn't it
11:45	? Okay . So we're gonna have to do one
11:48	which is going to be the adjacent , which is
11:52	this one running alongside . So let's make that seven
11:54	And the high pot news , that's going to be
11:56	X . Why is that ? You get the mindset
12:00	of how a teacher works nights inside . Is that
12:04	? So let's go through the motions anyway and work
12:06	this out . We know it's gonna be a cause
12:08	one , but let's work it out anyway as usual
12:10	because it's good , good method to be into .
12:12	Let's label the sides first . So the opposite over
12:15	here , we have the um , hi pot news
12:21	and we have the adjacent . And now let's work
12:25	out the true economic function . So we know that
12:28	some old hags can't always hack their old age .
12:37	Okay , We're dealing with always hacked it . So
12:40	we are dealing because good , it all worked out
12:42	. So because uh , 18 degrees equals always hack
12:51	I which is seven over X . Okay , Taking
12:56	a bit of a shortcut there already . Okay ,
12:58	so let's get X by itself . Okay , so
13:01	I'm gonna write that similar sort of thing up where
13:02	three equals six divided by two . And this time
13:06	the one we want is we want the one down
13:08	here , this one down here which equals this one
13:11	divided by this one . This one divided by this
13:14	one this one divided by this one , so X
13:18	87 divided by because island degrees equals let's work this
13:28	out there . Okay . Seven divided by 18 because
13:36	equals 7.36 . Alright , Cool . And occasionally can
13:43	look at and say , is there that's actually the
13:46	high point news there . That makes sense . It's
13:47	a it's a longer sort of length there , it's
13:50	a pretty shallow sort of angle . So it's not
13:52	gonna be a huge amount longer . So it's a
13:55	fairly reasonable sort of answer . So how did you
13:59	go with this ? Pretty good . Hopefully . Uh
14:02	anyway in the next video we're gonna be having a
14:04	look at working at using sides to work out unknown
14:07	angles . It's not much of its weak . It's
14:09	actually using a very , very similar sort of rules
14:13	here . Okay , so I hope to see you
14:15	then . Bye .

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