A
B
C
D
30o
60o
Foot of the
tower
Top of the
building
Foot of the
building
Top of the
Tower
30m
?
line of sight
line of sight
Tower
Building
Observer
Observer
Q. The angle of elevation of the top of a building from the foot of
the tower is 30o and the angle of elevation of the top of tower from
the foot of the building is 60o. If the tower is 30m high,
find the height of the building ?
Q. The angle of elevation of the top of a building
from the foot of the tower is 30o and the angle of
elevation of the top of tower from the foot of the
building is 60o. If the tower is 30m high, find the
height of the building ?
30m
A
B
C
D
30o
60o
?
AB
BC
30
BC
=
3
30
BC
=
3
30
BC
=
3
3
3
×
30
BC
=
3
3
10
BC
=
3
m
10
AB represents the height of the tower.
AB = 30m
CD represents the height of the building.
∠DBC = 30o
∠ACB = 60o
In right angled ΔABC,
tan 60o =
Sol.
Opposite
side
Adjacent side
Observe ∠ACB
tan 60o =
?
For ∠ACB
Opposite side →
Adjacent side →
AB
BC
Ratio of opposite side and Adjacent side reminds us of _________
‘tan’
∴
∴
∴
∴
∴
Consider ΔABC
Now, let us rationalise the denominator
Q. The angle of elevation of the top of a building
from the foot of the tower is 30o and the angle of
elevation of the top of tower from the foot of the
building is 60o. If the tower is 30m high, find the
height of the building ?
DC
BC
DC
=
DC
=
3
10
BC
=
3
m
3
1
10
3
10
3
DC
=
10 m
Height of the building is 10m
10
3
∴
∴
∴
In right angled ΔDBC,
tan 30o =
Observe ∠DBC
tan 30o =
?
1
For ∠DBC
Opposite side →
Adjacent side →
DC
BC
Consider ΔDBC
Sol.
30m
A
B
C
D
30o
60o
?
Opposite
side
Adjacent side
Ratio of opposite side and Adjacent side reminds us of _________
‘tan’