B
20
45º
D
Bottom of
tower
Top of
tower
60º
?
Height of the observer is neglected
A
C
line of sight
line of sight
Transmission
Tower
Q. From a point on the ground, the angles of elevation
of the bottom and the top of a transmission tower
fixed at the top of a 20m high building are 45º and
60º respectively. Find the height of tower.
(20 + x) m
Sol.
D
A
B
60º
C
20
45º
x
of elevation of the bottom and the top
of a transmission tower fixed at the top
of a 20m high building are 45º and 60º
respectively. Find the height of tower.
AB = 20m
AB represents the height of the building
BC represents the height of the
transmission tower.
Let BC be x m
In right angled ΔBAD,
tan 45º =
AB
AD
∴ 1
=
20
AD
∴ AD = 20 m
BC is part of AC
BC = AC – AB
To find AC, first we need to find AD
Opposite
side
Adjacent side
Observe ∠D
For ∠BDA
Opposite side →
Adjacent side →
tan 45o =
?
1
AB
AD
Ratio of opposite side and Adjacent side reminds us of _________
‘tan’
20m
?
Now, Consider ΔBAD
AC = AB + BC
∴ AC =
20
+ x
∴ AC =
Let us find AC
20m
In right angled ΔCAD,
tan 60º =
AC
AD
=
20 + x
20
∴
20 + x
∴
=
x
∴
=
– 20
x
20
∴
=
– 1)
x
20
∴
=
– 1)
AC =
(20 + x) m
Height of the transmission tower is 14.6 m
x
20
∴
=
× 0.73
x
14.6
∴
=
∴
(1.73
Sol.
of elevation of the bottom and the top
of a transmission tower fixed at the top
of a 20m high building are 45º and 60º
respectively. Find the height of tower.
D
A
B
60º
C
20
45º
x
For ∠CDA
Opposite side →
Adjacent side →
AC
AD
Observe ∠D
Ratio of opposite side and Adjacent side reminds us of _________
‘tan’
tan 60o =
?
Adjacent side
(x +20)m
Opposite
side