Multiple choice

A $1.2m$ tall girl spots a balloon moving with the wind in a horizontal line at a height of $88.2m$ from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is ${60}^{o}$. After some time, the angle of elevation reduces to ${30}^{o}$. Find the distance travelled by the balloon during the interval.

  1. $17\sqrt 2m$
  2. $34m$
  3. $58\sqrt 3m$
  4. $67m$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The height of the balloon from the girl's eye level is 88.2 - 1.2 = 87m. At 60 degrees, the horizontal distance is 87/tan(60) = 87/sqrt(3) = 29*sqrt(3). At 30 degrees, the distance is 87/tan(30) = 87*sqrt(3). The distance traveled is 87*sqrt(3) - 29*sqrt(3) = 58*sqrt(3)m.

AI explanation

The vertical height of the balloon from the girl's eye level is 88.2 meters minus 1.2 meters, which equals 87 meters. When the angle of elevation is 60 degrees, the horizontal distance is 87 divided by the square root of 3, which rationalizes to 29 times the square root of 3. When the angle reduces to 30 degrees, the new distance is 87 times the square root of 3, so the distance traveled is 87 times the square root of 3 minus 29 times the square root of 3, yielding 58 times the square root of 3 meters.

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