Multiple choice

Two light posts are of equal height. A person standing mid-way between the line joining their feet, observes the elevation of the posts to be $30^{0}$. After walking $12$ metres towards one of them, he observes that the same post now subtends an angle of $60^{0}$. Find the distance between them.

  1. $18\ m$
  2. $26\ m$
  3. $36\ m$
  4. $24\ m$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let height be h. Midpoint distance is d. tan(30) = h/d, so h = d/sqrt(3). After moving 12m, distance to one post is d-12, other is d+12. tan(60) = h/(d-12). sqrt(3) = (d/sqrt(3)) / (d-12). 3(d-12) = d. 3d - 36 = d. 2d = 36. d = 18. Total distance = 2d = 36m.

AI explanation

Let the height of the posts be h and the initial distance from the midpoint to each post be x. Using the 30 degree angle of elevation, we have tan 30 equals h over x, so h equals x divided by the square root of 3. After walking 12 meters towards one post, the new distance is x minus 12, and tan 60 equals h over (x minus 12), giving h equals the square root of 3 times (x minus 12). Equating the two expressions for h yields x minus 12 equals x divided by 3, which solves to x equals 18. The total distance between the posts is 2x, which is 36 m.

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