00:00
hi friends let's say you're standing near a tall building and you want to
measure its height let's say you're in front of Burj Khalifa which is the tallest
building in the world so how do you measure its height or let's say you're standing
on a bridge across a river how do you measure the width of the river to measure the
height of a tall building we'll have to go to the top and drop a long rope and
measure the length of the rope so it's not convenient right measuring the width of
the river is even harder because you
00:35
have to stand on opposite banks with a long rope so it's not practical
but if you know trigonometry then it's really easy in this video we learn how to
apply trigonometry to measure Heights and distances I'm going to make the concepts
really easy for you and after you watch this video try the quiz and the top 3
questions on this topic links are given below the video before we look at the
applications of trigonometry first let's quickly revise the basics of trigonometry
so as you can see for a right angle triangle where the right
01:14
angle is really important in trigonometry because we can define these
ratios only when you have a right angle triangle so we define the basic ratios sine
theta cos theta tan theta as perpendicular ba hypotenuse base by hypotenuse and
perpendicular by base and then here we have their reciprocals cosec theta SEC theta
and cot theta let's see how we can use these trigonometrical ratios to find heights
and distances without actually measuring them so let's dive right into it let's say
we are standing in front of
01:50
Burj Khalifa or any other building let's mark the building as a B now we
are going to observe the top of the building a from a point of observation on the
ground oh so oh is the point of observation now if you join oh ay then this line is
called the line of right because we are looking at the top of the building a from
the point Oh now through Oh draw a horizontal line OB so you're basically joining
the point of observation Oh to the base of the building B now what is the angle
between lines a B and O B that's right as you
02:37
can see angle B is 90 degree why because the building is standing
vertically so the angle it makes with the ground is 90 degrees but let's say
instead of bulge Khalifah this was the Leaning Tower of Pisa would angle B be still
90 degree no we can apply this only for the buildings that are standing straight
now the angle here this angle is called angle theta the angle of elevation so
that's the angle between line o a and line OB so theta is the angle of elevation
here now we can measure this angle using a
03:20
surveying instrument so we measured this angle and let's say angle theta
was 60 degree okay and let's say we measured the distance from o to the base of the
building be using a measuring tape and the distance was 480 meters so let's see how
we can apply trigonometry to find the height of Burj Kalifa without going to the
top of the building to solve any question on heights and distances the first
important thing is to draw nice diagram so for our question where we wanted to find
the height of the Burj
, 03:56
Kalifa building I've drawn a diagram here so here our building is a B and
remember we were given o was the point of observation which is 480 meters from the
base of the building B okay so you should draw this line OB and Mark the distance
there and this angle of elevation since you are looking up from the point of
observation o to the top of the building so this angle here was given to us as 60
degree and so what is a right angle triangle yeah a B oh and why is angle B 90
degree because remember the building
04:37
is standing appendicular to the ground right so that's a 90 degree here
because we need a right angle triangle to use our trigonometrical ratios so now
let's mark what do we need to find in the diagram so we need to find the height of
the building a B so let's label that as X since that's our unknown okay and now to
solve for X the simple trick is take the ratio of what is not known to you so what
is unknown and what is given right so let's take this so what's that ratio gonna be
it's gonna be a B so the side a B by the side Oh B
05:23
right and so we have the ratio X by 480 meters here right so let me mark
that up here so what we don't know by what is given now this ratio of this sides
you need to find out what trigonometrical ratio are you using so to identify that
let's take a look here in this triangle a OB can you see that the side a b is the
perpendicular right so it's the perpendicular in this triangle so I'm gonna mark it
with P and what is OB over here that's right it's the base of the triangle so let's
label that with B so
06:20
we are basically looking at X by 480 which is basically the perpendicular
by the base of this right angle triangle so which trigonometrical ratios are we
talking about that's right it's going to be tan theta right and what is our theta
over here can you see the angle theta here is 60 degree so I'm going to write tan
of 60 correct so now basically once we solve this we can easily get X so let's go
ahead and do that and so do you know what is the value of tan 60 that's right it's
going to be root 3 so you
07:06
need to learn up these values so we have X by 480 is equal to root 3 so
let me copy that down here so therefore X is going to be 480 into root 3 meters and
if you solve that you're going to get actually so let's substitute the value so 480
into 1 point 7 3 2 so that's the value of root 3 and if you multiply these numbers
X is going to be 831 0.36 meters so that's the height of our building right so it's
really simple as you can see what we did here you just look for what you don't know
and what's
08:01
given you take that trigonometrical ratio and then you need to identify
what ratio is it so for us it was perpendicular by base so we are working basically
with tan theta so that's tan 60 and you substitute the values and once you solve
for it you can easily get the height of the building so the height of Burj Kalifa
is 830 1.36 meters according to our question now let's take a look at this question
so we have that shadow of a 10 meter long pole is 10 root 3 meter find the angular
hi friends let's say you're standing near a tall building and you want to
measure its height let's say you're in front of Burj Khalifa which is the tallest
building in the world so how do you measure its height or let's say you're standing
on a bridge across a river how do you measure the width of the river to measure the
height of a tall building we'll have to go to the top and drop a long rope and
measure the length of the rope so it's not convenient right measuring the width of
the river is even harder because you
00:35
have to stand on opposite banks with a long rope so it's not practical
but if you know trigonometry then it's really easy in this video we learn how to
apply trigonometry to measure Heights and distances I'm going to make the concepts
really easy for you and after you watch this video try the quiz and the top 3
questions on this topic links are given below the video before we look at the
applications of trigonometry first let's quickly revise the basics of trigonometry
so as you can see for a right angle triangle where the right
01:14
angle is really important in trigonometry because we can define these
ratios only when you have a right angle triangle so we define the basic ratios sine
theta cos theta tan theta as perpendicular ba hypotenuse base by hypotenuse and
perpendicular by base and then here we have their reciprocals cosec theta SEC theta
and cot theta let's see how we can use these trigonometrical ratios to find heights
and distances without actually measuring them so let's dive right into it let's say
we are standing in front of
01:50
Burj Khalifa or any other building let's mark the building as a B now we
are going to observe the top of the building a from a point of observation on the
ground oh so oh is the point of observation now if you join oh ay then this line is
called the line of right because we are looking at the top of the building a from
the point Oh now through Oh draw a horizontal line OB so you're basically joining
the point of observation Oh to the base of the building B now what is the angle
between lines a B and O B that's right as you
02:37
can see angle B is 90 degree why because the building is standing
vertically so the angle it makes with the ground is 90 degrees but let's say
instead of bulge Khalifah this was the Leaning Tower of Pisa would angle B be still
90 degree no we can apply this only for the buildings that are standing straight
now the angle here this angle is called angle theta the angle of elevation so
that's the angle between line o a and line OB so theta is the angle of elevation
here now we can measure this angle using a
03:20
surveying instrument so we measured this angle and let's say angle theta
was 60 degree okay and let's say we measured the distance from o to the base of the
building be using a measuring tape and the distance was 480 meters so let's see how
we can apply trigonometry to find the height of Burj Kalifa without going to the
top of the building to solve any question on heights and distances the first
important thing is to draw nice diagram so for our question where we wanted to find
the height of the Burj
, 03:56
Kalifa building I've drawn a diagram here so here our building is a B and
remember we were given o was the point of observation which is 480 meters from the
base of the building B okay so you should draw this line OB and Mark the distance
there and this angle of elevation since you are looking up from the point of
observation o to the top of the building so this angle here was given to us as 60
degree and so what is a right angle triangle yeah a B oh and why is angle B 90
degree because remember the building
04:37
is standing appendicular to the ground right so that's a 90 degree here
because we need a right angle triangle to use our trigonometrical ratios so now
let's mark what do we need to find in the diagram so we need to find the height of
the building a B so let's label that as X since that's our unknown okay and now to
solve for X the simple trick is take the ratio of what is not known to you so what
is unknown and what is given right so let's take this so what's that ratio gonna be
it's gonna be a B so the side a B by the side Oh B
05:23
right and so we have the ratio X by 480 meters here right so let me mark
that up here so what we don't know by what is given now this ratio of this sides
you need to find out what trigonometrical ratio are you using so to identify that
let's take a look here in this triangle a OB can you see that the side a b is the
perpendicular right so it's the perpendicular in this triangle so I'm gonna mark it
with P and what is OB over here that's right it's the base of the triangle so let's
label that with B so
06:20
we are basically looking at X by 480 which is basically the perpendicular
by the base of this right angle triangle so which trigonometrical ratios are we
talking about that's right it's going to be tan theta right and what is our theta
over here can you see the angle theta here is 60 degree so I'm going to write tan
of 60 correct so now basically once we solve this we can easily get X so let's go
ahead and do that and so do you know what is the value of tan 60 that's right it's
going to be root 3 so you
07:06
need to learn up these values so we have X by 480 is equal to root 3 so
let me copy that down here so therefore X is going to be 480 into root 3 meters and
if you solve that you're going to get actually so let's substitute the value so 480
into 1 point 7 3 2 so that's the value of root 3 and if you multiply these numbers
X is going to be 831 0.36 meters so that's the height of our building right so it's
really simple as you can see what we did here you just look for what you don't know
and what's
08:01
given you take that trigonometrical ratio and then you need to identify
what ratio is it so for us it was perpendicular by base so we are working basically
with tan theta so that's tan 60 and you substitute the values and once you solve
for it you can easily get the height of the building so the height of Burj Kalifa
is 830 1.36 meters according to our question now let's take a look at this question
so we have that shadow of a 10 meter long pole is 10 root 3 meter find the angular
