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QJEEM21Mae2c1: JEE Main 2021 Mathematics - Class 12 JEEM21Mae2c1 Solution: Two vertical poles are 150 m apart and the height of one is…

Two vertical poles are 150 m apart and the height of one is three times that of the other. If from the middle point of the line joining their feet, an observer finds the angles of elevation of their tops to be complementary, then the height of the shorter pole (in meters) is :

Multiple Choice Options

  • A 30
  • B 25
  • C 20 3\sqrt 3
  • D 25 3\sqrt 3

Step-by-Step Verified Solution

JEE Main 2021 (Online) 24th February Morning Shift Mathematics - Height and Distance Question 19 English Explanation
∴\therefore tan⁡(90−θ)=x75\tan (90 - \theta ) = {x \over {75}}

and tan⁡θ=3x75\tan \theta = {{3x} \over {75}}

As cot⁡θ.tan⁡θ=1\cot \theta .\tan \theta = 1

∴\therefore x75.3x75=1{x \over {75}}.{{3x} \over {75}} = 1

⇒x=253\Rightarrow x = 25\sqrt 3

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