Multiple choice

The angle of elevation of the top of a tower at a distance of $\displaystyle \frac{50\sqrt{3}}{3}$ metres from the foot is $\displaystyle 60^{\circ}$. Find the height of the tower

  1. $\displaystyle 50\sqrt{3}$ metres
  2. $\displaystyle \frac{20}{\sqrt{3}}$ metres
  3. $-50$ metres
  4. $50$ metres
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D Correct answer
Explanation

Height = distance * tan(angle). Height = (50 * sqrt(3) / 3) * tan(60) = (50 * sqrt(3) / 3) * sqrt(3) = (50 * 3) / 3 = 50 meters.

AI explanation

Using the trigonometric ratio for height and distance, tan(60 degrees) equals the height of the tower divided by the distance from the foot. We have sqrt(3) = height divided by (50*sqrt(3)/3). Multiplying sqrt(3) by (50*sqrt(3)/3) gives 150/3, which results in a height of 50 metres.

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