Examples: Application of Trigonometry- 1 Video Lecture - Class 10

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this video please make sure that you
have watched part 1 a second example the
contractor plans to install two sliders
for the children to play in the bar for
the children below five years she
prefers to have slider to stop is a
fight 1.5 meter incline at 30 degree for
elder children she wants to have a
steeper slide it is 3 meter and angle
essentially what is the length of each
slides so let's draw this is the slide
at the bigger slider which you get so
there are two scenarios in one scenario
the height is 1 point 5 meter in another
scenario the height is 3 meter also the
angle is different and so this length
will also differ so what we can do it's
draw triangle on this so that we can get
a clear picture so if you see this is a
triangle here not correct they have two
scenarios this is theta actually manga
which makes this is theta they are two
scenarios it is 30 degree and succeeding
they are two scenarios in one case it is
13 yarn is 60 and height also they are
two scenarios in one case it is 1 point
5 meter in one case it is 3 meter and we
have to find this right length of the
slip so let me draw their two keys
actually if we throw in this fashion law
here case 1 and case 2 case 1 the height
is 1 point 5 meter this is for age 5
year - height is 1 point 5 and the angle
is 30 degree in case 2 the height is 3
meter and the angle is 60 degree we have
to find this length actually in both of
these l1 and this is ending correct so
now you see theta this theta is an angle
picture
this guy's hypotenuse this guy is
perpendicular and this guy's base
somebody here also this guy is
hypotenuse
this guy's perpendicular and this guy's
base so we have a relation we know l1 we
know this 1.5 you know theta so we have
some looking for something via relation
in between H and P so let's again go by
our formula pundit Bathory Prashad
arrey arrey both so h and p the relation
is not with sine theta correct so we use
sine theta so in case 1 we will see sine
30 degree is it going to be by H P here
is 1.5 and as share is L 1 and sine 30
is nothing but 1 by 2 so 1 by 2 is equal
to 1.5 by n1 or you get L 1 is equal to
1.5 minute - but is 3 meter so this is
my length in the first case in the
second case where it is 4 in Derby / 5
year plus here also I use the same
formula sine 60 equal to P by H but
particular here is 3 meter and H
hypotenuse ins length n 2 sine 60 Xanthi
but roots if I do this is equal to 3 by
2 or I get n 2 is equal to 3 into 2 by
root 3 correct so let me rationalize
this by multiplying by root 3 root 3 so
this root 3 root 3 becomes 3 3 n 3
cancels so this is 2 root 3 metre so in
case 2 the length is 2 root 3 so in case
1 he has the length of the slide will be
3 meter and incased with the leather
side will be u root 3 meter let us take
on example the angle of elevation of the
tower top of the tower from a point in
the ground which is 30 meter away from
the foot of the tower is 30 meter here
to find the
height of the top take this this is the
tower this is the point there is 30
meter this point is 30 meter from the
tower okay and the st. say the angle of
elevation from this point the top of
tower is 13 so let us draw the triangle
here this is the angle of elevation
actually just all this is right triangle
being it because the tower is vertical
and this angle is 40 degree we are told
and this length is 30 meter we have to
find high or guitarra
so if we consider cheetah and suppose
this triangle is ABC claim is trying V B
and C it sees the angle of reference
this is hypotenuse because side opposite
the 90 angle so this becomes
perpendicular and this becomes this
correct and height of the tower is
exercise now we want to find a relation
between T and B by because P is X and B
is 30 so we again go by the formula
funded by the refresh our array array
Bowl so P and V is in this one this is
nothing but sine cos tan triste and this
will use the formula tan theta that is
tan 30 degree is equal to D by B and
that is nothing but X by 30 or tan 30 is
nothing but 1 by root 3 is equal to X by
30 or what I get X is equal to 30 by
root Li you can rationalize this by
multiplying and dividing by root 3 so
this becomes 30 by 3 root key that is 10
root 3 meter that is my answer so height
of the tower is 10 root 3 metre very
simple just try to understand the
problem draw a right triangle and then
try to see what you are looking for you
have X you have 30 and you have time
one regulation that is you have T you
have B so since you have t NV you go for
tan 30 because tan is something which
has p NV one just put this form line get
that where is it
we take home example a kite is flying at
the height 60 meter above the ground
this is the kite string attached to the
kite is temporarily tied to the point in
the ground this is account ground
actually the inclination of the string
with the ground is 60 degree this angle
makes is 60 degree need to find the
length of the string as I mean there is
no slack in this game so what we can do
let's form a triangle first this is a
point of time okay this is a triangle we
have and let's name this a DNC all right
the question says the inclination 60
degree so this angle is actually height
is 60 meter so this height is 60 meter
is given to me correct
we have to find what length this is the
length we have to find this like now
since in this triangle right triangle
ABC if see the reference this side is
height this would be perpendicular and
this side would be base correct now I
have to drive relation between H and P
because I have to find edge and I have
been given P and your angle against a
new block bundle by the repechage for a
red ball
H NP is in this one this is a sign so
you use the sign so you say sine 60
degree is equal to H by sorry II by H
right equal to B by H and P is here 60 +
ecchi here the length of the string or
sine 60 is nothing but root 3 by 2 is
equal to 60 by L or what again L is
nothing but 60 into 2 by root 3 you can
rationalize this by multiplying and
dividing
what you get is 16 - 2 is 1 20 by 3 root
3
they say it's Canton 40 so you get 40
root 3 meter so length of the string is
40 root 3 very simple what we have done
we have got the sign by sign because
perpendicular was given we have to find
the hypotenuse and the relation between
perpendicular and hypothesis is best
expressed by sine theta so we have used
sine theta all right thank you
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