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QJEEM21Ma3713: JEE Main 2021 Mathematics - Class 12 JEEM21Ma3713 Solution: A vertical pole fixed to the horizontal ground is divided in…

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 :

Multiple Choice Options

  • A 12 15\sqrt {15}
  • B 12 10\sqrt {10}
  • C 8 10\sqrt {10}
  • D 6 10\sqrt {10}

Step-by-Step Verified Solution

JEE Main 2021 (Online) 31st August Morning Shift Mathematics - Height and Distance Question 11 English Explanation

Let height of pole = 10 ll

tan⁡α=3l18=l6\tan \alpha = {{3l} \over {18}} = {l \over 6}

tan⁡2α=10l18\tan 2\alpha = {{10l} \over {18}}

2tan⁡α1−tan⁡2α=10l18{{2\tan \alpha } \over {1 - {{\tan }^2}\alpha }} = {{10l} \over {18}}

use tan⁡α=l6⇒l=725\tan \alpha = {l \over 6} \Rightarrow l = \sqrt {{{72} \over 5}}

height of pole = 10l=121010l = 12\sqrt {10}

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