Let AB represent a building of height h metre with A being its top B being its bottom Let A rsquo B ...........

Quantitative Aptitude (CDS) Trignometry

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?

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

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Explanation:

In triangle AA’C:
tan45⁰ = A′C/AC= x/AC => x/AC=1 => AC = BB’ = x => x = d
Adding h on both sides, we get
h + x = h + d
So, h + x > d
Hence statement 1 is correct.
In triangle A’BB’:
If we take angle be 45⁰
Then, tan45⁰ = A′B′/BB′= (h+x)/d => (h+x)/d=1 => d = h + x
But, by statement 1, this is not possible.
Thus, θ ≠ 45⁰
Now, either θ < 45⁰ or θ > 45⁰
Let, θ = 60⁰ > 45⁰
In triangle A’BB’
tan 60⁰ = A′B′/BB′= h+x => √3 = h+x => d√3 = h + x ……. (i)
Let, θ = 30⁰ < 45⁰
In triangle A’BB’
tan 45⁰ = A′B′/BB′= (h+x)/d => √3 = (h+x)d => d√3=(h + x) ……. (ii)
From (i), we can conclude that either LHS = RHS or, LHS > RHS
But, from (ii), clearly LHS < RHS
Hence, we cannot conclude that the angle of depression of B from A’ is less than 45⁰
Hence statement 2 is incorrect.
Hence option (3)