Q. A TV tower stands vertically on a bank of a canal. From a point on the
other bank directly opposite the tower, the angle of elevation of the top
of the tower is 60°. From another point 20 m away from this point on the
line joining this point to the foot of the tower, the angle of elevation of the top
of the tower is 30º. Find the height of the tower and the width of the canal.
60o
30o
Height of the observer is neglected
?
?
line of sight
line of sight
A
D
B
C
20 m
observer
From a point on the other bank directly opposite
the tower, the angle of elevation of the top of the
tower is 60°. From another point 20 m away from
this point on the line joining this point to the foot
of the tower, the angle of elevation of the top of
the tower is 30º. Find the height of the tower and
the width of the canal.
Sol.
Let the height of tower be ‘h’ m
Let the width of the canal be ‘x’ m
Distance (DC) = 20 m
In right ΔABC,
tan 60º
=
AB
BC
∴
=
h
x
∴
h
=
A
D
B
C
30º
60º
20 m
x
h
Opposite
side
Adjacent side
Observe ∠C
Ratio of opposite side and Adjacent side reminds us of _________
‘tan’
For ∠ACB
Opposite side →
Adjacent side →
AB
BC
tan 60o =
?
Consider ΔABC
From a point on the other bank directly opposite
the tower, the angle of elevation of the top of the
tower is 60°. From another point 20 m away from
this point on the line joining this point to the foot
of the tower, the angle of elevation of the top of
the tower is 30º. Find the height of the tower and
the width of the canal.
In right ΔABD,
tan 30º
=
AB
BD
∴
1
=
h
x + 20
∴
x + 20
=
h
∴
x + 20
=
x
×
x + 20
=
3x
20
=
2x
x
=
10
h
=
x
=
× 10
h
=
10
Width of the canal is 10 m
and Height of the tower is 17.3 m
x
h
=
x
∴
∴
∴
h
=
10
1.73
×
= 17.3
(x + 20)
10 m
Sol.
A
D
B
C
30º
60º
20 m
h
Adjacent side
Opposite
side
Consider ΔABD
Observe ∠D
For ∠ADB
Opposite side →
Adjacent side →
AB
BD
Ratio of opposite side and Adjacent side reminds us of _________
‘tan’
tan 30o =
?
1