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?
(3+√3) : (1+√3) : 1
(√3-1) : 1 : (3-√3)
(3-√3) : 1 : (√3-1)
(3-√3) : (√3-1) : 1
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 tan60= √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