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Good day students
in this clip we are going to be going over an example
we are going to be dealing with a composite case where we have the
triangle that is a combination of the two special triangles
the 30-60-90 and the 45-45-90
special triangles okay and that is what is illustrated in this figure right here
below so the instructions are for us to find the value
of x and y alright. So in order for us to do this
problem what we have to do is basically split this triangle
into two separate triangles and then treat them independently
now in order for us to be able to find the
the value of y we need to find the length of this segment
since we already have x taken how about we call this segment a
and then we have to find the length of this segment
How about we call this
b then we can call this segment right here c
alright so in order to find y
a and b conbined
alright and you have another triangle here so lets go ahead and do all these
these two triangles separately. I am just going to make a
rough sketch of he right side so lets see
we have this is the
30 60 90 triangle right here
here alright
lets focus on this one first. We need to find this portion. How long is this portion
this segment
this portion of y right here so that
we can then shift our attention to b and og
right so how long is that portion
so this is 18 you know that the hypotenuse is 18
this is a 90 degree angle this is 30 if this is 30
30 then this angle here must be 60 degrees. So this is the
30 60 90 triangle this is side is a.
and this side here is c it would be beneficial
in for us to bring the measure to see because it is a triangle we have been
we know the measurable site at all and we at least one side
in order to be able to find the other sides using the special
triangle. Alright so let us find a and c
in this triangle right here. Now before we do that let us draw the base
of the 30-60-90 triangle. I am going to draw it on the side right here
here lets use the green marker
30 60 90 triangles gonna guide how I'm gonna populate the denominators of the sides
of the sides
so the base 30-60-90 triangle is as follows
opposite the bigger of the two
angles that are not right is 60 degrees
and opposite that side is root three. and then opposite the smallest angle
angle 30 degrees is one and then opposite the hypotenuse
is two alright. This is the base
30 60 90 triangle ok this is the model that we use to create the other one
the
this is similar to this but just scaled up by a certain factor.
alright so what I'm going to do is I am going to set it up as follows:
underneath
the ninety degree angle I mean
the side opposite the the ninety degree angle I am going to put a two. Because you notice that there is a
tow opposite the ninety degree angle of the base triangle
opposite the sixty degree the side opposite the sixty degree I am going to put it over root 3
3 and opposite the 30 degrees
I will put it over one
so let's start by finding by
find a
we are going to set the ratio that we are missing a side
now we the variable here and the ratio that
which is this region right here okay so let's go ahead and set up the region and
it's also gonna have I'll
a over root three is equal to 18 over 2
so to get a isolated we multiply both sides by root 3
root three on the left and root three on the left
while doing that we can often see here that needs to be divided up
K still the street theory reading right now one
in one any real effort a.m. the left side
equals now on the right side to use you 1 I'm
getting to do it here ninth grades so we have assigned major
eighty being equal to no rain read three okay
right now I let's go ahead and find see
points even
or exit *** Theory gonna set up up the ratio
animal see si amor 1
equals arm the review that we know the value to both sides
18 over to you 18 over to you
alright let's go ahead and so pristine see everyone is you see
1802 is nine okay
the haps CE in
writes me back them in and I'm going to be between them in back into the
triangle and it still can know
while iraq that acts a in a taxi
yeah it's up on this portion ring here
seeing naive
since working here naive and a
aids magritte 3 cities perjuring here night bridge
3 okay all right now let's eat your attention to the second triangle this is
the body by
fortified ninety triangle let's go ahead n
us get it over here we treated independently
the 12 very poor want to you
re or alright mate with you there
pounds yet again we had 12
green or by anybody right here he can see that
iraq we separated from one another right now
thing and
re-think the body by provide many travel biz
portion of this bull composite triangle rights-era leanna
I'll forty by here in and decided
X anyway agree to call this thing you right
when the major decided see but we already know what see
what is the value see CE from the on the triangle where we could determine
is the ball tonight okay all right now
so the struggle for X Mb we're going to
create our beaches a triangle the base model
for the 45-point but may try and go let's put it on site right here
and it was great how we can properly denominators right through and is going
to a little
about Big East forty-five 45
ninety triangle right here
okay and then we have his body
by
business but if I were here me that's pretty
I opposite reported by its we have wanted it's the one
anything the one in a bid in ninety degrees we have ripped to you
are the net with you beats 45 45 90 triangle
right to know that come here on the side opposite 25 2013 19:21
he's going to be a long one in the fed up within ninety degrees
is I'm
is I read few character but it's colder
weeks to you alright so this is what we get
because the teacher and will are similar let's sort it might bind need
on be from its fine be in
trying site be
begin at nicole is set up to rate you that Smith they have their own
with the rate you that doesn't have any here was an All which is my number one
said bulgari look at that I for buying the minutes that the ratio of be overall
wine alright Indian
equals my number one miro is being a novel won its ninth seal
they happen right now it's buying
X define act
what we're going to do is to reach you X over reads
to you the quote from 9am-1
to get X isolated mounted by Woodside by Rick to you
re to re to you in Beantown
its treaties cancel out final answer X
we could be equal to 98 routine to do that the measures that the sides
I'll the weight by forty by ninety triangle
Kang let's be there back in in there
be I turns out the BBC miss see
the 9 that there to these poor sharing here is denying
innate X he is
u9 routine Villa Rica exit nine read to you
re: alright so the question to ask is defined X&Y
so we can see from the sheep that X is equal to 9 with you
NY he's actually it's some
these base against 30 60 90 truck when the bees and it's pretty purple
man-made trials is going to be with someone these to combine silly
that answer is going to be 9 plus behind reads
3 alright still that's the major arm
I'll up beside up this composite
triangle that we have right here right
in them books our acts in
thanks so much for taking the time to which this presentation pp subscribe to
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thanks again for watching had a wonderful day