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On level ground the shadow of a vertical pole is exactly one third as long as the pole. The Sun's altitude θ then satisfies:

Competition practiceTrigonometry
  • A60° < θ < 75°
  • Bθ = 60°
  • C30° < θ < 45°
  • Dθ = 30°

Step-by-Step Solution

The altitude satisfies tanθ = height/shadow = 3. Since tan60° = √3 ≈ 1.732 and tan75° = 2 + √3 ≈ 3.732, the value 3 sits between them, so θ lies strictly between 60° and 75° (in fact θ ≈ 71.6°). At exactly 60° the shadow would be 1/√3 ≈ 0.577 of the height, far more than a third; a short shadow means a HIGH Sun, so the two options below 45° have the relationship backwards — at 30° the shadow would be √3 ≈ 1.73 times the height.
Answer: A) 60° < θ < 75°

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