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Q.

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) :

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a

$12 \sqrt{15}$

b

$12 \sqrt{10}$

c

$8 \sqrt{10}$

d

$6 \sqrt{10}$

answer is B.

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Detailed Solution

Let height of pole $= 10 l$
$\tan α = \frac{3 l}{18} = \frac{l}{6}$
$\tan 2 α = \frac{10 l}{18}$ Question Image
$\frac{2 \tan α}{1 - \tan^{2} α} = \frac{10 l}{18}$
$use \tan α = \frac{l}{6} = \Rightarrow l = \sqrt{\frac{72}{5}}$
$height of pole = 10 l = 12 \sqrt{10}$

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