Multiple choice

Two vertical lamp-posts of equal height stand on either side of a road 50m wide.At a point P on the road between them.Elevation of the tops of the lamps are 60 &30.Find the distance of P from the lamp post which makes angle of 60?

  1. $25m$
  2. $12.5m$
  3. $16.5m$
  4. $20.5m$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let h be the height of the posts and x be the distance from the 60-degree post. Then h/x = tan(60) = sqrt(3) and h/(50-x) = tan(30) = 1/sqrt(3). So h = x*sqrt(3) and h = (50-x)/sqrt(3). Equating: x*sqrt(3) = (50-x)/sqrt(3) => 3x = 50-x => 4x = 50 => x = 12.5.

AI explanation

Let the height of both lamp-posts be h, and let the distance from point P to the closer lamp-post be x. From the elevation angles, h equals x times the tangent of 60 degrees, and h also equals the quantity 50 minus x times the tangent of 30 degrees. Equating the two expressions gives x times the square root of 3 equals the quantity 50 minus x divided by the square root of 3, which solves to 3x equals 50 minus x. Therefore, x is 50 divided by 4, which is 12.5 meters.

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