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UPSC CDS Math Height and Distances Questions
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© examsnet.com
Question : 22
Total: 25
From a certain point on a straight road, a person observes a tower in the west direction at a distance of 200 m. He walks some distance along the road and finds that the same tower is 300 m south of him. What is the shortest distance of the tower from the road?
[2014 CDS-II]
300
√
13
m
500
√
13
m
600
√
13
m
900
√
13
m
Validate
Solution:
Let AD be the shortest distance of the tower from road BC.
In right ΔABC,
B
C
=
√
(
200
)
2
+
(
300
)
2
=
√
1300
=
100
√
13
m
Area of
∆
ABC
=
1
2
×
AB
×
AC
=
1
2
×
200
×
300
m
2
Also, Area of ∆ABC
=
1
2
×
BC
×
AD
=
1
2
×
100
√
13
×
ADm
2
∴
1
2
×
100
√
13
×
A
D
=
1
2
×
200
×
300
⇒
A
D
=
60000
100
√
13
=
600
√
13
m
© examsnet.com
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