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04/02/2022 1:47 pm
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A vertical pole fixed to the horizontal ground is divided in the ratio 3 : 7 by a mark on it with lower part shorter than the upper part. If the two parts subtend equal angles at a point on the ground 18 m away from the base of the pole, then the height of the pole (in meters) is :
(1) 12√15
(2) 12√10
(3) 8√10
(4) 6√10
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04/02/2022 1:55 pm
Correct answer: (2) 12√10
Explanation:
Let height of pole = 10ℓ
tanα = \(\frac{3ℓ}{18}\) = \(\frac{ℓ}{6}\)
tan2α = \(\frac{10ℓ}{18}\)
\(\frac{2 tanα}{1 - tan^2α}\) = \(\frac{10ℓ}{18}\)
use tanα = \(\frac{ℓ}{6}\) ⇒ ℓ = \(\sqrt{\frac{72}{5}}\)
height of pole = 10ℓ = 12√10