Multiple choice

From the top of a cliff $24\ m$ height, a man observes the angle of depresion of a boat is to be $60^{0}$. The distance of the boat from the foot of the cliff is

  1. $8\sqrt{3}\ m$
  2. $8\sqrt{2}\ m$
  3. $8\sqrt{5}\ m$
  4. $8\ m$
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A Correct answer
Explanation

In a right triangle, tan(60) = height / distance. sqrt(3) = 24 / distance. Distance = 24 / sqrt(3) = 8 * sqrt(3).

AI explanation

The angle of depression to the boat equals the angle of elevation from the boat to the top of the cliff. In the resulting right triangle, tan(60) = 24 / distance. Since tan(60) is sqrt(3), we have sqrt(3) = 24 / distance. Solving for the distance gives distance = 24 / sqrt(3), which rationalizes to 8 * sqrt(3). The result is 8 * sqrt(3) m.

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