Multiple choice

A tower of height $'h'$ standing vertically at the center of a square f side length $'a'$ subtends the same angle $'\theta '$ at all the corner points of the square. Then

  1. $2h^{2} = a^{2} tan^{2} \theta$
  2. $a^{2} = 2h^{2}tan^{2} \theta$
  3. $a^{2} = 2h^{2}cot^{2} \theta$
  4. $2a^{2} = h^{2}cot^{2} \theta$
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A Correct answer
AI explanation

The distance from the center of the square to any corner is half the diagonal, which equals a / sqrt(2). The tower of height h forms a right triangle with this distance, giving tan(theta) = h / (a / sqrt(2)). Squaring both sides gives tan^2(theta) = 2h^2 / a^2. Multiplying by a^2 yields the result 2h^2 = a^2 * tan^2(theta).

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