Multiple choice

From the top of a building $h$ metre high, the angle of depression of an object on the ground has a measure $\theta$. The distance of the object from the building is

  1. $h\cos { \theta } $ metre
  2. $h\sin { \theta } $ metre
  3. $\tan { \theta } $ metre
  4. $h\cot { \theta } $
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D Correct answer
Explanation

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

AI explanation

The angle of depression equals the angle of elevation from the object to the top of the building, so we use the tangent ratio. We have tan(theta) equals the height h divided by the horizontal distance. Solving for this distance gives h divided by tan(theta), which simplifies to h times cot(theta). The distance of the object is therefore h cot theta metre.

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