Q.
1.2m
30o
A
B
C
D
E
P
R
A 1.2 m tall girl spots a balloon moving with the wind in a horizontal
line at a height of 88.2 m from the ground. The angle of elevation of the
balloon from the eye of girl is 60º. After some time, angle of elevation reduces to 30º. Find the distance travelled by the balloon during the interval.
line of sight
Horizontal line
88.2m
88.2m
line of sight
Q
?
60o
A 1.2 m tall girl spots a balloon moving with
the wind in a horizontal line at a height of
88.2 m from the ground. The angle of
elevation of the balloon from the eyes of
girl is 60º. After some time, angle of elevation
reduces to 30º. Find the distance travelled
by the balloon during the interval.
Q.
87 m
88.2 m
Height of balloon from the ground
(AB) = 88.2 m
Height of the girl (PE) = 1.2 m
PE =
QA =
RC
BQ = BA – QA
=
88.2
– 1.2
= 87 m
In right ΔBQP,
tan 60º =
BQ
PQ
∴
=
87
PQ
∴
PQ
=
87
∴
PQ
=
87
×
∴
PQ
=
87
3
∴
PQ
=
P
B
E
A
C
R
D
Q
1.2 m
60º
30º
3
3
3
3
3
3
29
3
= 1.2m
∴ BQ
Observe ‘BA’
Find : QR
QR is a part of PR
Observe ‘QR’
QR = PR – PQ
PQ belongs to right angled triangle BQP
Ratio of opposite side and Adjacent side reminds us of _________
‘tan’
tan 60o =
?
29
3
Opposite
side
Adjacent side
Observe ∠P
BA is made up of
BQ and QA
For ∠BPQ
Opposite side →
Adjacent side →
BQ
PQ
Sol.
Now, let us rationalise the denominator
88.2 m
In right ΔPRD,
tan 30º =
DR
PR
∴
=
87
PR
1
∴
PR
=
87
– PQ
PR
∴
Distance travelled by the balloon is
100.34 m
3
3
∴
QR
29
3
–
=
87
3
QR
=
58
3
P
E
A
C
R
Q
1.2 m
60º
30º
Opposite
side
29
3
∴ QR
=
58
× 1.73
∴ QR
=
100.34 m
A 1.2 m tall girl spots a balloon moving with
the wind in a horizontal line at a height of
88.2 m from the ground. The angle of
elevation of the balloon from the eyes of
girl is 60º. After some time, angle of elevation
reduces to 30º. Find the distance travelled
by the balloon during the interval.
Sol.
QR = PR – PQ
Ratio of opposite side and Adjacent side reminds us of _________
‘tan’
PR belongs to
right angled triangle PRD
tan 30o =
?
1
Observe ∠P
For ∠P
Opposite side →
Adjacent side →
DR
PR
Q.
Adjacent side
87 m
QR =
B
D