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UPSC CDS Math Height and Distances Questions
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© examsnet.com
Question : 3
Total: 25
Consider a regular hexagon ABCDEF . Two towers are situated at B and C. The angle of elevation from A to the top of the tower at B is 30°, and the angle of elevation to the top of the tower at C is 45°, What is the ratio of the height of towers at B and C ?
[2019 CDS-I]
1 :
√
3
1 : 3
1 : 2
1 : 2
√
3
Validate
Solution:
Let the height of towers at B and C be h and k, respectively, and the side of hexagon be x.
h
x
=
tan
30
°
h
=
x
√
3
A
C
2
=
x
2
+
x
2
–
2
x
2
cos
120
°
=
2
x
2
+
2
x
2
cos
60
°
=
3
x
2
⇒
A
C
=
√
3
x
k
A
C
=
tan
45
°
=
1
⇒
k
=
A
C
=
√
3
x
h
k
=
x
√
3
√
3
x
=
1
3
=
1
:
3
© examsnet.com
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