A vertical pole fixed to the ground is divided in the ratio 4:5 by a mark on it with lower part shorter than the upper part. If the two parts subtend the same angle at a place on the ground, 16 m away from the base of the pole, what is the height of the pole?
Let CB be the pole and point D divides it such that BD: DC = 4: 5 Given that AB = 16 m Let the two parts subtend equal angles at point A such that 
CAD = BAD = θ CAB = 2 θ 
BD/DC=AB/AC ⇒ 4/5 = 16/AC then AC = 20 CB= √ (AC2−AB2) CB = √ (20)2 – (16)2 = √ 144 = 12m
