Multiple choice

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

  1. $17.3$ m
  2. $57.96$ m
  3. $17.8$ m
  4. $173$ m
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A Correct answer
Explanation

tan(30) = height / distance. 1/sqrt(3) = h / 30. h = 30 / sqrt(3) = 10 * sqrt(3) = 10 * 1.732 = 17.32 m.

AI explanation

Let the height of the tower be h. Using the basic trigonometric ratio for the right-angled triangle formed, tan 30 degrees equals h divided by 30. Since tan 30 degrees is 1 divided by the square root of 3, we have h equals 30 divided by the square root of 3. Rationalizing the denominator gives h equals 10 times the square root of 3. Using the approximation of 1.732 for the square root of 3, the height is 17.3 m.

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