Multiple choice

The angle of elevation of the top of a tower from point at a distance of $100$ metres from its foot on a horizontal plane is found to be $\displaystyle 60^{\circ}$. Find the height of the tower

  1. $173.2 m$
  2. $196 m$
  3. $144 m$
  4. $123.2 m$
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A Correct answer
Explanation

Height = distance * tan(60). tan(60) = sqrt(3) approx 1.732. Height = 100 * 1.732 = 173.2 m.

AI explanation

Using the angle of elevation formula, tan(60 degrees) = height / base. Given the base is 100 m and tan(60 degrees) is sqrt(3), we have sqrt(3) = height / 100. This gives height = 100 * sqrt(3) m. Since the square root of 3 is approximately 1.732, multiplying it by 100 yields the result 173.2 m.

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