Multiple choice

The angle of elevation of the top of a tower at a distance of $300$ metres from its foot on a horizontal plane is found to be $30^o$. The height of the tower is

  1. $173m$
  2. $300\sqrt 3$m
  3. $100m$

  4. None
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A Correct answer
Explanation

tan(30) = Height / Distance. 1/sqrt(3) = H / 300. H = 300 / sqrt(3) = 100 * sqrt(3) = 100 * 1.732 = 173.2m.

AI explanation

Using the trigonometric ratio for height and distance, tan(30 degrees) equals the height of the tower divided by 300. We set up the equation 1/sqrt(3) = height / 300. Multiplying 300 by 1/sqrt(3) results in 173.2 m, making the height approximately 173 m.

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