30, 45 degree ratio Video Lecture - Class 10

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we will now study trigonometric ratio
some specific angles you'll find
trigonometric ratio 45 degree how did
equally and steadily and will also find
zero degree and 90 degree all these
angles are very much required in solving
equations so we'll go hold these three
it's more about 45 so this angle is 45
degrees angles this angle is 90 degree
this angle does will fortify why because
some of angle is 180 what if I this is
90 we already know so this angle has to
be 45 some of these training big 90 cut
the sides the angles are equal besides a
b and b c will be equal let us assume
the length of ABC X 2 EC it also creates
a correct C we have done that we have
seen that to find diplomatic ratios all
the women TV show the first thing we
will do is we have to find the site of
alignment so if we can find the sides of
this triangle we can find a diplomatic
issue so here we can see that this is
right triangle so we can say that AC
square is equal to AV square plus BC
square correct and this is nothing but X
square plus X square or AC is equal to
root of 2x but that is nothing but root
2 X so AC is nothing but root 2 X so let
me assume sign a because sine 40 K is
sign the expediter let me assume a as my
angle so a is mapping of reference this
is edge side adjacent will be B's this
is B and side up a little Perpignan so
this is perpendicular so I match PN be
correct so again I'll use the power log
one with the three
Rashaad hurry hurry
born correct sign cause tan this is
Kazakh sick cotton so I have sine theta
is equal to B by H that is X by P is
equal to X h by root 2 X that comes out
to be 1 by 2 mu V cos theta over 2 B by
H V is X a chisel 2x look at also 1 by 2
tan theta this is theta actually is you
can do P by B so it comes out to be P is
X V is X 1 minus ma similarly you can
find who think Rita is equal to H by P
hyp
but this root 2 X by X that is do
similarly we have SEC Teta is equal to I
have H by P H by B you can do 2 X by X
that was a root cool so only cot theta
is nothing but B by B even B is equal to
X by X like this so cut all the values
of theta and they all theta is equal to
45
so our sine 40 here is going to 1 by
root 2 cos 40 by 1 by root 2 tan 45 1
Kozik 40 by root 2 SEC 45 root 2 and
caught 45 all the values are for
dividing now let's find diplomatic ratio
for 30 degree M 60 so ABC is equal to
angle all sides 60 degree all rangas
viridi and all sides of length 2 so
skewing this is true
and if you see this is 30 degree you are
30 degree this angle bisector so this
sides will be equal right good angle is
equal this is the and this is also G
this is 30 degree this is actually
actually both the sides are congruent if
you see why because this is 30 degree
this is 60 degree angles are matching
and one side is common ad
so both sides both the triangle are
congruent so both the length will be
when VD could be equal to DZ so but LM
not a any got soul in this to me now
let's find this length of AD ad will be
equal to root off in this triangle to
take Langley if it is a right triangle
so top AV square minus DD square all
right so this becomes u dog to a square
minus e square that is root of 4 is 4 n
minus H square and this root of 3 is
square that is root 3 so this is nothing
but root 3 now you see my life is simple
why because I have a triangle AB theta
it should agree and of all the sides
root 3a a and 2 similarly if I take this
angle theta for degree I also have all
the three sides so let me take first
this angle theta so I'm trying to find I
am taking B as my frame of reference so
this will be H liquid drawn this again
here correct B a and D this is 90 degree
and this is 60 correct this will be H nu
since this is my ring of reference this
will be perpendicular and this V miss
now this is doing two in circles jinke
and this is a have all the sides now if
I want to find sine B or sine 60 degree
this would be equal to it is a fall
again on live bird refresh on for a her
a more sine cos tan Han Kasich say
cotton fine theta is nothing but P by H
there is P by H whereas P do trillion
movie what is H to it so this becomes 3
my save earlier defined costly or cause
it's to degree this Lhasa become D by H
this will be B by H what is the value of
B a and H is 2 e so this becomes 1 right
who
similarly tan B or tan 60 degree there
is nothing but D by B but it's p u3 a
what is V a so this becomes so I have
all this value sine cos and tan 60 sale
early if you want to find a KO sex is
really nothing but 1 by sine so it will
be receive over of this particular rule
by du is 2 by root 3 correct and sick 60
degree is 1 by cos is she that is 1 by 1
by 2 is 2 and caught 60 degree is 1 by
10 that is 1 by so I have all the value
of 60 degrees correct I'll use circle
now let me find 430 degrees so if I take
angle a as metric of reference and put
like this and all same we actually a VD
the angle a is my frame of reference
this is my Deary me
so I participate if I can a is my friend
over friends this side becomes base and
this side becomes perpendicular correct
and the length is anyway constant this
way this is a and this is root 3 now I
have to find this is 30 degree actually
sign a that is nothing word sign or TV
for the velocity living sine 30 31 T by
H P by H what is the value of e a H 2 a
this becomes 1 right
similarly cause of the or cause of 30 do
the same thing this will equal to B by H
by H so in this case B is routine a and
H is to it so this becomes root 3
writing tan of a will be equal to tan 30
and tan is nothing but P by B correct
please what a B's word to tree this
becomes 1 by since we have sine cos and
tan of ka we can find cause again that
is 1 by assigning so one by one by two
other is true that is sine Casa Caribe
SEC 30 degree of equal to one by cos 30
degree that is 1 by root 3 by 2 that is
2
and caught of 30-degree with equal to 1
by 10:30 here is 1 by 1 by root C that
is so what all the values the values of
cosine 30 SEC 30 court 30 which is sign
that he calls 30 tannic does we have all
the values of sine 30 sine 60 cause that
T cos 60 1030 1060 that means away of
all the Dignam attic ratios of 38 see
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