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= √ (AC^{2}−AB^{2}) CB = √ (20)^{2} – (16)^{2} = √ 144 = 12m

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