Multiple choice

From the top of a building $h$ metres, the angle of depression of an object on the ground is $\alpha$, the distance of the object from the foot of the building is

  1. $h\cot\alpha$
  2. $h\tan\alpha$
  3. $h\cos\alpha$
  4. $h\sin\alpha$
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A Correct answer
Explanation

In a right triangle formed by the building height (h), the ground distance (d), and the line of sight, the angle of depression equals the angle of elevation. Thus, tan(alpha) = h / d, which implies d = h / tan(alpha) = h * cot(alpha).

AI explanation

The angle of depression equals the angle of elevation from the object to the top of the building. In the right triangle formed, tan(alpha) = h / distance. Solving for the distance gives distance = h / tan(alpha), which simplifies to h * cot(alpha). The result is h * cot(alpha).

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