Multiple choice

Two poles of equal heights are standing opposite to each other on either side of the road which is $80m$ wide. From a point between them on the road, the angles of elevation of the top of the poles are ${60}^{o}$ and ${30}^{o}$ respectively. Find the height of the poles and the distances of the point from the poles.

  1. $21\sqrt{11}m, 60 m$
  2. $15\sqrt{7}m, 56 m$
  3. $20\sqrt{3}m, 60 m$
  4. $15\sqrt{2}m, 45 m$
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C Correct answer
AI explanation

Let the point on the road be at a distance x from the first pole and 80 - x from the second pole. Using trigonometric ratios for height, h = x tan(60) and h = (80 - x) tan(30). Substituting the values gives x sqrt(3) = (80 - x) / sqrt(3), which simplifies to 3x = 80 - x, yielding x = 20 meters. The height of the poles is 20 sqrt(3) meters, and the distances from the point to the poles are 20 meters and 60 meters.

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