Examples (Part 5) - Application of Trigonometry, CBSE Class 10 Mathematics Video Lecture

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take one more example as observed from
the top of a 75 meter lighthouse from
sea level the angle of depression of
ships are T in 45-degree one sheet is
exactly fine another shape find this in
victim to ships so let's take this water
here we have this lighthouse and there
is the ship here and the other ship is
exactly behind the other ship this ship
this is non worship and the questions is
the angle of depression of the Toshiba
30 to 45 degrees let's drop us into line
here because from the top they are
asking for the angle of depression so
see so I'm going to talk so from the top
we got the horizontal 9 and this angle
is 45 degree and this angle is the
videos this angle is 30 the pker angle
is of the heading correct what we have
to do we have to find this in between
these two ships what we can do it's a
major triangle first this is a high
angle loan let's name this triangle a B
C so we have to find this distance C
correct and since this angle is 45 so I
will be fortified what does this line 89
line a and V D both of other two lines
we have value and this angle is 13 so
this angle will also be 30 degree
correct and the height of the tower is
75 meter given so what we can do we can
find this distance d1 we can find the
whole distance d2 so you can find bc and
we can find reading pi we have this in
this triangle ABC we know this angle we
know this length in
BC simmering in triangle a B D you know
this angle we know this fight a you can
find me he so we have B D we have DC
begin piety let's do this
now if 45 degrees the this angle C
supreme of reference in triangle ABC D
will be right in triangle ABC if sees
the ring of reference this guy becomes
sniper two years you see this becomes
perpendicular and this become space
since I have to find BC so I'm dealing
with P and V under the pressure on array
her a whole pn v is tan so I need to
find time again so I can say and 45 here
E is equal to e YB so in this case P is
nothing but v b and b is nothing but VC
and AV is nothing but 75 and we see
something it of mind and time 45 is 1 so
from this what we get VC is equal to 75
meter that does my BC this is done
correct knowledge strictest triangle abd
vertically B similarly here also he is
pertains the claim of reference this a D
side become hyperness this perpendicular
and really site becomes this so again we
are dealing with perpendicular waves so
tan theta so I'll say tan theta that is
30 degree is equal to e by B
perpendicular is nothing but V V and V
is nothing but V D this so a B is
nothing but 75 and we need something we
have to find and this is a liver time 13
that is 1 by root 3 so if you solve this
you get VD is equal to 75 G correct so
if I find to find this distance V D is
nothing but CD and CD is nothing but V
DV minus VC and that is nothing but 75
- 75 and that is nothing but 75 into mu
3 minus 1 and then unit is meter that is
answer so the distance between two
boards is 75 into root 3 minus 1 very
simple just draw this triangle since you
have the triangle you have the angles we
have one side we can get the other sites
and we can get a CD very easy the only
thing is you have to understand the
problem and draw this diagram if you're
able to understand the problem that is
as observed from the top of 75 meter
lighthouse so you take this value top
position from this point you draw
angular dispersion the depression you
choose or in the line you draw the
angles and then you get this let's take
on my example one point two meter tall
girl spots a balloon moving with the
wind in the horizontal line at the
height 88 point 2 meter from the crown
see please note the height of the girls
are also given and height of the balloon
is also given the angle of elevation of
the balloon from eyes with a girl at a
760 degree after some time the angle of
elevation is 30 degree we have to find
the distance traveled by value of doing
the interval this is the girl whose
height is one point two two there is a
balloon she spots this vellum and
currently the belorus 30 degree
elevation sorry 60 degree elevation so
this angle is 60 degree now with the
grain this balloon will go in this
direction so better and go in this
direction after some time the angle of
elevation of this fellow is become 30
degree we have to find the distance
traveled by the bed of the center let us
draw the triangle law here this is the
triangle we have to find this distance
and give this name a b c
the e we have to find this distance this
distance seed we have to find C because
the balloon traveled from this point
this point that is named and he is going
to see correct so what we can do is we
had told at the height of the belorus
88.2 from the ground so you take this
point from to here this high that was f
EF is 88.2 but DF is one point to the
height of a girl's this distance to be
eighty eight point two minus one point
because the height of the girl leaves of
time this becomes 87 so this point is it
is said that is given D is 87 and this
length is also instant now it's very
simple asking this triangle ABC if you
can find this the BC in strangle edct
can find VD we have BC we have reading
can subtract to get resistance correct
spoon do the same thing in triangle ABC
is B is the trip of reference this will
be happen is the perpendicular and this
will be base correct I know carbon if I
go I find base I'm trying to find
relation between perpendicular in base
content but the Refresh table array has
a bone PNB is tan
so you stand here so I say tan in this
case angle essentially is equal to P by
V here P is EC then B is BC and AC is 87
and BC we don't know and tan 60 is root
3 so we get VC is equal to 87 my to to
you can rationalize this by multiplying
and dividing by 3 so root t2 3 is 3 3 by
87 by 3 is 29
this times 29 so I got this value VC is
equal to 29
this time now I have to find VD so we
will say in flying will be easy that we
can try a same thing
so we'll say tan 30 why because we are
dealing with P and V here so tan 30 will
be equal to e by be here P is II D and V
is V be correct and et is going to be 87
and BD something we have to fight and
tan 30 is not very angry so if we solve
this we get VD is equal to 87 this BD
whole thing is but 87 so we have to find
distance we have to find the distance
and the distance traveled is nothing but
C D then C D is nothing but VD minus BC
you see C D is nothing but the VD think
minus PC so we know VD VD is nothing but
V 2 7 root 3 and we know BC that is 29
would subtract this this becomes 58 and
that is the unit will be in meter
because we are talking about meters
meter and that means the distance to
have the pattern is 58 root 3 metre in
this duration because the world was
standing in the same position so you
observe the balloon has changed its
angle then the balloon has moved from
this position insufficient allene was 60
degree then become 30 degree so the
distance type of error is 58 thank you
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