Multiple choice

A balloon is observed simultaneously from three points A B and Con a straight road directly under it. The angular-elevation at B is twice that at A and the angular elevation at C is thrice that at A If the distance between A and B is 200 metres and the distance between B and C is 100 metres, find the height of the balloon.

  1. $50 \sqrt{3}$m
  2. $50 $m
  3. $150 \sqrt{3}$m
  4. $100 \sqrt{3}$m
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let h be the height and x be the distance from the point directly under the balloon to A. Using tan(theta) = h/dist, we have h/x = tan(A), h/(x-200) = tan(2A), and h/(x-300) = tan(3A). Solving these trigonometric equations yields h = 100 * sqrt(3).

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