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JEE Main 201912 AprilEvening Shift
Exam
JEE Main
Year
2019
Date
12 April
Shift
Evening Shift
Subject
Mathematics
Chapter
Heights and Distances

JEE Main 2019 · 12 April · Evening Shift · Mathematics · Heights and Distances

The angle of the top of a vertical tower standing on a horizontal...

The angle of the top of a vertical tower standing on a horizontal plane is observed to be 45°45 ° from a point A on the plane. Let BB be the point 30m30m vertically above the point A. If the angle of elevation of the top of the tower from BB be 30°30 ° , then the distance (in m) of the foot of the tower from the point AA is:The angle of the top of a vertical tower standing on a horizontal plane is observed to be 45 ° from a point A on the

Options

  1. A15(3+3)15\left(3 + \sqrt{3}\right)
  2. B15(1+3)15\left(1 + \sqrt{3}\right)
  3. C15(5−3)15\left(5 - \sqrt{3}\right)
  4. D15(3−3)15\left(3 - \sqrt{3}\right)

Correct answer

A. 15(3+3)15\left(3 + \sqrt{3}\right)

Step-by-step solution

The angle of the top of a vertical tower standing on a horizontal plane is observed to be 45 ° from a point A on the
tan45o=1=x+30y⇒x+30=ytan{45}^{o} = 1 = \dfrac{x + 30}{y} ⇒ x + 30 = y ......(i)
tan30o=13=xy⇒x=y3tan{30}^{o} = \dfrac{1}{\sqrt{3}} = \dfrac{x}{y} ⇒ x = \dfrac{y}{\sqrt{3}} ......(ii)
from (i) and (ii) y = 15\left(3 + \sqrt{3}\right)
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