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UPSC CDS Math Height and Distances Questions
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© examsnet.com
Question : 18
Total: 25
The angle of elevation of a cloud from a point 200 m above a lake is 30° and the angle of depression of its reflection in the lake is 60°. The height of the cloud is
[2015 CDS-I]
200 m
200 m
400 m
600 m
Validate
Solution:
Let the height of the cloud above the sea level be h m.
Here, AF = 200 m, CE = (h - 200) mand DE = (h + 200) m
∠CFE = 30° and ∠DFE = 60°
In right ΔCFE,
t
a
n
30
°
=
C
E
F
E
⇒
1
√
3
=
h
−
200
F
E
⇒
F
E
=
√
3
(
h
−
300
)
In right ΔDFE,
t
a
n
60
°
=
D
E
F
E
⇒
√
3
=
h
+
200
√
3
(
h
−
200
)
⇒
3
h
−
600
=
h
+
200
⇒
2
h
=
800
⇒
h
=
400
m
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