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UPSC CDS Math Height and Distances Questions
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© examsnet.com
Question : 8
Total: 25
A man, standing at a point X on the bank XY of a river that cannot be crossed, observes a tower to be N α° E on the opposite parallel bank. He then walks 200 m along the bank to the point Y towards East, and finds the tower to be N β° W. From these observations, the breadth of the river will be (Given that tan a° = 2 and tan β° = 0.5)
[2017 CDS-II]
60 m
70 m
80 m
90 m
Validate
Solution:
Let AB be the width of the river
In right ΔABX
tan
α
=
A
B
X
B
⇒
X
B
=
A
B
2
=
0.5
A
B
....(1)
In right ΔABY,
tan
β
=
A
B
B
Y
⇒
B
Y
=
A
B
0.5
=
2
A
B
....(2)
Adding (1) and (2), we have
0.5
A
B
+
2
A
B
=
X
B
+
B
Y
⇒
2.5
A
B
=
X
Y
=
200
m
⇒
A
B
=
200
2.5
=
80
m
Thus, the breadth of the river is 80 m.
© examsnet.com
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