A
B
C
D
P
Q
30o
60o
60m
Height of the person
is neglected
reflection
Distance of
cloud from
lake surface
=
Distance of its reflection from lake surface
Observer
Horizontal line
line of sight
cloud
line of sight
is 30o and the angle of depression of the reflection of cloud in
the lake is 60o. Find the height of the cloud from lake surface.
a point 60m above a lake is 30o and
the angle of depression of the reflection
of cloud in the lake is 60o. Find the height
of the cloud from lake surface.
A
B
P
Q
C
D
30o
60o
60m
A represents observer above the lake.
AB = 60 m
P represents the cloud.
∠PAD is the angle of elevation.
∠PAD = 30o
Q represents the reflection of cloud.
∠DAQ is the angle of depression.
∠DAQ = 60o
In right angled ΔADP,
What does point ‘A’
represent?
Observer
PD
AD
x – 60
=
3
1
AD
x
x
AD
=
(x – 60)
3
m
What does point ‘P’
represent?
cloud
What does point ‘Q’
represent?
Reflection
of the cloud
tan 30o =
3
1
?
(x – 60)
3
60m
□ABCD is a rectangle
AB = CD = 60m
PD + CD = PC
∴ PD + 60 = x
∴ PD = (x - 60)m
Let PC = x
PC = CQ
∴ CQ = x
(x-60)
Opposite
side
Adjacent side
Observe ∠A
Ratio of opposite side and Adjacent side reminds us of _________
‘tan’
For ∠PAD
Opposite side →
Adjacent side →
PD
AD
Observe PC
PC is made up of PD and CD
Consider ΔADP
∴
∴
Sol. :
a point 60m above a lake is 30o and
the angle of depression of the reflection
of cloud in the lake is 60o. Find the height
of the cloud from lake surface.
∴
∴
∴
∴
∴
∴
∴
∴
A
B
P
Q
C
D
30o
60o
60m
x
x
DQ
AD
x + 60
=
3
(x – 60)
3
3x – 180 =
2x =
x = 120
3 (x – 60) =
x + 60
x + 60
3x – x =
60 + 180
240
The height of cloud above the lake is 120 m
PC =
120 m
tan 60o =
?
3
(x – 60)
3
In right angled ΔAQD,
60m
QD = CQ + CD
QD = (x + 60)m
(x-60)
Opposite
side
Adjacent side
Observe ∠A
Ratio of opposite side and Adjacent side reminds us of _________
‘tan’
For ∠DAQ
Opposite side →
Adjacent side →
DQ
AD
QD is made up of QC and CD
Observe QD
(x + 60)
Consider ΔAQD
Sol. :