Multiple choice

A tower, stationed at the center of a circular park, is casting a shadow. A person standing at the east side of the tower is making an angle of 45° with the top of the tower. Simultaneously, another person, stationed at the west side of the tower, is making an angle of 60° with the top of the tower. The height of the tower is 400 feet. What is the approximate shortest distance between these two persons? Assume both persons are of negligible dimensions.

  1. 425

  2. 452

  3. 631

  4. 842
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C Correct answer
Explanation

The tower height h = 400. For the person at 45 degrees, the distance from the tower base is d1 = h / tan(45) = 400. For the person at 60 degrees, the distance is d2 = h / tan(60) = 400 / sqrt(3) approx 230.94. The total distance is d1 + d2 = 400 + 230.94 = 630.94, which rounds to 631.

AI explanation

Using trigonometric ratios, the distance from the tower to the person on the east is 400 divided by tan 45 degrees, which is 400 feet. The distance from the tower to the person on the west is 400 divided by tan 60 degrees, which equals 400 divided by root 3 feet. Since they stand on opposite sides, the total distance is 400 plus 400 divided by root 3, which approximates to 400 plus 230.94, or 630.94 feet; this rounds to 631 feet.

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