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UPSC CDS Math Height and Distances Questions
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© examsnet.com
Question : 10
Total: 25
From the top of a building 90 m high, the angles of depression of the top and the bottom of a tree are 30° and 45° respectively. What is the height of the tree ?
[2017 CDS-I]
30
√
3
m
90
−
30
√
3
m
90
+
30
√
3
m
60
+
30
√
3
m
Validate
Solution:
Here, AB is the building and CD isthe tree.Here, AB is the building and CD is the tree.
Let the height of the tree be h m.
AB = 90 m and CD = h m.
∴ BE = AB – AE = AB – CD
= (90 – h) m
In right ΔABC
tan
45
°
=
1
=
A
B
A
C
⇒ AC = 90m
In right ΔBDE
tan
30
°
=
1
√
3
=
B
E
D
E
⇒
1
√
3
=
90
−
h
90
(DE=AC)
⇒
90
−
h
=
30
√
3
⇒
h
=
(
90
−
30
√
3
)
m
© examsnet.com
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