XAT 2022 Question Paper | Quantitative Aptitude and Data Interpretation

XAT Previous Year Paper | XAT QADI Questions | Question 24

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Question 24 : A tall tower has its base at point K. Three points A, B and C are located at distances of 4 metres, 8 metres and 16 metres respectively from K. The angles of elevation of the top of the tower from A and C are complementary.

What is the angle of elevation (in degrees) of the tower's top from B?

  1. 45
  2. 15
  3. 30
  4. We need more information to solve this.
  5. 60

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Explanatory Answer

Three triangles
It is given that the angle of elevation from A and C are complementary.
The angles ∠TKA = ∠TKB = ∠TKC = \(90^{\circ}\)
Hence ∠TAK = ∠KCT and ∠KTC = ∠KAB
So that the ΔTKC and ΔAKT are similar triangles
\(\frac{T K}{A K}\) = \(\frac{K C}{T K}\) = \(\frac{C T}{T A}\) 
\(\frac{T K}{A K}\) = \(\frac{K C}{T K}\)
\(T K^{2}=4 \times 16\)
TK = 8
So ΔTKB is an isosceles triangle.
Therefore angle of elevation at B is \(45^{0}\)

The answer is '45'

Choice A is the correct answer.

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