Quantitative Aptitude – Geometry – The topmost point of a perfectly vertical pole

XAT 2021 Exam Paper – Quantitative Aptitude – Geometry – The topmost point of a perfectly vertical pole

Q. The topmost point of a perfectly vertical pole is marked A. The pole stands on a flat ground at point D. The points B and C are somewhere between A and D on the pole. From a point E, located on the ground at a certain distance from D, the points A, B and C are at angles of 60, 45 and 30 degrees respectively. What is AB : BC : CD?
  1. (3+√3) : (1+√3) : 1
  2. (√3-1) : 1 : (3-√3)
  3. (3-√3) : 1 : (√3-1)
  4. (3-√3) : (√3-1) : 1
  5. 1 : 1: 1

Answer: (3-√3) : (√3-1) : 1

Solutions:

Let DE =x also , angle DEA = 60, DEB = 45 , and DEC = 30
Using tan 60 = AD/DE
AD = DE tan⁡60= √3x
Similarly BD = x and CD=x/√3
AB =AD-BD= √3 x-x=x(√3-1)
BC = BD-CD=x-x/√3=x(√3-1)/√3
Thus AB : BC :CD = (√3-1) ∶((√3-1))/√3 ∶1/√3=(3-√3): (√3-1):1

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