A worker rides a builder's hoist that climbs the outside of a tower. When his eye is 12 m above the level ground he sees a bench on the ground at an angle of depression of 30°. When his eye reaches 36 m, the angle of depression of the same bench is:

The bench does not move, so its horizontal distance is fixed: d = 12·cot30° = 12√3 ≈ 20.78 m. At the new eye height, tan(depression) = 36/(12√3) = 3/√3 = √3, so the angle is 60°. The height has tripled but the angle has only doubled — angles and heights are not proportional, so 90° (tripling the angle to match the height) is wrong, and 90° would in any case mean looking straight down. Choosing 30° assumes the angle is a property of the bench rather than of the sight line, and 45° would need the eye height to equal 12√3 ≈ 20.8 m.