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JEE Main201815 Apr 2018Evening ShiftMathematicsHeights and DistancesActual

A tower T₁ of height 60 ~m is located exactly opposite to a tower T₂ of height 80 ~m on a straight road. From the top of T₁ , if the angle of depression of the foot of T₂ is twice the angle of elevation of the top of T₂ , then the width (in m ) of the road between the feet of the towers T₁ and T₂ is

Options

  1. A20 2
  2. B10 2
  3. C10 3
  4. D20 3

Correct answer

D. 20 3

Step-by-step solution

Let the distance between T₁ and T₂ be x From the figure E A=60 ~m (T₁ ) and D B=80 ~m (T₂ ) D E C= and B E C=2 Now in D E C , = D C A B = 20 x and in B E C , 2 = B C C E = 60 x We know that 2 = 2 1-( )^2 aligned & 60 x = 2 ( 20 x ) 1- ( 20 x )^2 & x^2=1200 x=20 3 aligned

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