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UPSC CDS Math Height and Distances Questions
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© examsnet.com
Question : 7
Total: 25
Let AB represent a building of height h metre with A being its top, B being its bottom. Let A'B' represent a tower of height (h + x) metre (x > 0) with A' being its top and B' being its bottom. Let BB' = d metre. Let the angle of elevation of A' as seen from A be 45°
Consider the following statements :
Statement I: h + x > d
Statement II: The angle of depression of B as seen from A' is less than 45°.
Which one of the following is correct in respect of the above statements ?
[2017 CDS-II]
Both Statement I and Statement II are true and Statement II is the correct explanation of Statement I
Both Statement I and Statement II are true but Statement II is not the correct explanation of Statement I
Statement I is true but Statement II is false
Statement I is false but Statement II is true
Validate
Solution:
Let the angle of depression of B as seen from A’ be θ
In right ΔAA'C
tan
45
°
=
A
′
C
A
C
⇒
1
=
x
d
⇒
x
=
d
⇒
h
+
x
>
d
Hence, statement I is correct.
In right ΔBA'B',
tan
θ
=
A
′
B
′
B
B
′
=
h
+
x
d
⇒
tan
θ
>
1
⇒
θ
>
45
°
Hence, statement II is incorrect.
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