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?
Explanation:
Let ED = √3x
In triangle CDE, tan 30 = CD3x ⇒ CD = x
In triangle BDE, tan 45 = BD3x ⇒ BD = 3x ⇒ BC = 3x - x
In triangle ÖDE, tan 60 = AD3x ⇒ AD = 3x ⇒ AB = 3x - 3x
AB : BC : CD = (3 - √3) : (√3 - 1) : 1
Help us build a Free and Comprehensive Preparation portal for various competitive exams by providing us your valuable feedback about Apti4All and how it can be improved.