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NDA2018MathematicsHeights and DistancesActual

A spherical balloon of radius r subtends an angle at the eye of an observer, while the angle of elevation of its centre is . What is the height of the centre of the balloon (neglecting the height of the observer)?

Options

  1. Ar ( 2 )
  2. Br ( 4 )
  3. Cr ( 2 )
  4. Dr ( 2 )

Correct answer

A. r ( 2 )

Step-by-step solution

Let ' A ' be the position of eye. Let ' O ' be the centre of spherical balloon. Let ' h ' be the height of centre of balloon. From figure, in OAD , 2 = OD OA = r OA aligned & OA = r 2 ...(1) & In OAB , = OB OA = h OA & ~h = OA & = r 2 ...from (1) aligned

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