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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 \mathrm{~m} away from the base of the pole, then the height of the pole (in meters) is :
Option: 1 8 \sqrt{10}
Option: 2 6 \sqrt{10}
Option: 3 12 \sqrt{10}
Option: 4 12 \sqrt{15}

Answers (1)


In\: \triangle ABC ;\tan \theta = \frac{3x}{18}= \frac{x}{6}---\left ( 1 \right )
In\: \triangle ABD ;\tan 2\theta = \frac{10x}{18}= \frac{5x}{9}
\Rightarrow \frac{2\tan \theta }{1-\tan ^{2}\theta }= \frac{5x}{9}
\Rightarrow \frac{2\times \frac{x}{6}}{1-\frac{x^{2}}{36}}= \frac{5x}{9}
\Rightarrow 108= 180-5x^{2}\Rightarrow 5x^{2}= 72
\Rightarrow x = 6\sqrt{\frac{2}{5}}\Rightarrow 10x = 6\sqrt{\frac{2}{5}}\times 10= 12\sqrt{10}
option (3)

Posted by

Kuldeep Maurya

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