10 m
30 m
45o
A
C
B
D
E
Observer
line of sight
Horizontal line
?
width 10 metres. From the top of the first building, which is
30 metres high, the angle of elevation of top of the second is 45o .
What is the height of the second building ?
Top of the
second building
on either side of a road of width 10 metres.
From the top of the first building, which is
30 metres high, the angle of elevation of
top of the second is 45o .
What is the height of the second building ?
C
E
D
A
B
45o
10 m
30 m
Sol.
The height of the second
building is 40 m
CE
AE
CE
10
AB and CD represents the heights of two buildings.
AB = 30 m
BD represents the width of the road.
BD = 10 m
A represents the position of the observer.
∠CAE is the angle of elevation.
∠CAE = 45o
□ABDE is a rectangle.
AB = DE = 30 m
BD = AE = 10 m
In right angled ΔCEA,
tan 45o =
1
=
10 m
CE
=
CD
=
CE
+
ED
∴
CD
=
10
+
30
∴
CD
=
40 m
∴
10 m
30 m
Opposite
side
Adjacent side
Observe ∠CAE
Ratio of opposite side and Adjacent side reminds us of _________
‘tan’
For ∠CAE
Opposite side →
Adjacent side →
CE
AE
Consider ΔCEA
tan 45o =
?
1
Observe CD
CD is made up of CE and ED
∴
∴