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UPSC 2017 CDS I Math Paper
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© examsnet.com
Question : 100
Total: 100
From an aeroplane vertically over a straight horizontal road, the angles of depression of two consecutive kilometre-stones on the opposite sides of the aeroplane are observed to be a and p. The height of the aeroplane above the road is
[2017 CDS-I]
t
a
n
α
+
t
a
n
β
t
a
n
α
t
a
n
β
t
a
n
α
t
a
n
β
t
a
n
α
+
t
a
n
β
c
o
t
α
c
o
t
β
c
o
t
α
+
c
o
t
β
c
o
t
α
+
c
o
t
β
c
o
t
α
c
o
t
β
Validate
Solution:
Let AB be the height of the aeroplane above the road. Suppose C and D are the positions of the two consecutive kilometer stones on the opposite side of the aeroplane
Here, CD = 1 km In right ΔABC
tan
α
=
A
B
B
C
⇒
B
C
=
A
B
tan
α
.....(1)
In right ΔABD,
tan
β
=
A
B
B
D
⇒
B
D
=
A
B
tan
β
......(2)
Adding (1) and (2), we have
A
B
tan
β
+
A
B
tan
α
=
B
C
+
B
D
=
C
D
⇒
A
B
(
tan
α
+
tan
β
tan
α
tan
β
)
=
1
⇒
A
B
=
tan
α
tan
β
tan
α
+
t
a
n
β
© examsnet.com
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