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MHT CET202619 April 2026Evening ShiftMathematicsHeights and DistancesActual

The lengths of the shadows of a tree of height p, thrown by sun's rays at three different moments are p, 2p and 3p. The sum of the angles of elevation of the sun's rays at these three moments is equal to...

Options

  1. A2 3
  2. B3 2
  3. C4
  4. D2

Correct answer

D. 2

Step-by-step solution

Let the angles of elevation of the sun's rays at the three moments be ₁ , ₂ , and ₃ . From the given information, the height of the tree is p and the lengths of the shadows are p , 2p , and 3p . ₁ = p p = 1 ₁ = 4 ₂ = p 2p = 1 2 ₃ = p 3p = 1 3 Using the tangent addition formula for ₂ and ₃ : ( ₂ + ₃) = ₂ + ₃ 1 - ₂ ₃ Substituting the values: ( ₂ + ₃) = 1 2 + 1 3 1 - 1 2 1 3 = 5 6 5 6 = 1 Since ₂ and ₃ are acute angles, ₂ + ₃ = 4 . Therefore, the sum of the angles of elevation is: ₁ + ₂ + ₃ = 4 + 4 = 2

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