Question

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?

A 20 meter Correct Answer Incorrect Answer
B 18 meter Correct Answer Incorrect Answer
C 15 meter Correct Answer Incorrect Answer
D 12 meter Correct Answer Incorrect Answer

Solution

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 angle CAD =  angle BAD = θ angle CAB = 2 θ BD/DC=AB/AC ⇒ 4/5 = 16/AC then AC = 20 CB= √ (AC2−AB2) CB = √ (20)2 – (16)2 = √ 144 = 12m

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