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QJEEM22Madeeb: JEE Main 2022 Mathematics - Class 12 JEEM22Madeeb Solution: Let a vertical tower A B of height 2 h stands on a horizontal…

Let a vertical tower AB of height 2h stands on a horizontal ground. Let from a point P on the ground a man can see upto height h of the tower with an angle of elevation 2α. When from P, he moves a distance d in the direction of AP→, he can see the top B of the tower with an angle of elevation α. If d=7h, then tan⁡α is equal to

Multiple Choice Options

  • A 5−2
  • B 3−1
  • C 7−2
  • D 7−3

Step-by-Step Verified Solution

JEE Main 2022 (Online) 27th July Morning Shift Mathematics - Height and Distance Question 7 English Explanation

ΔAPM gives

tan⁡2α=hx ..... (i)

ΔAQB gives

tan⁡2α=2hx+d=2hx+h7 ...... (ii)

From (i) and (ii)

tan⁡2α=2.tan⁡2α1+7.tan⁡2α

Let t=tan⁡α

⇒t=22t1−t21+7.2t1−t2

⇒t2−27t+3=0

t=7−2

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