2015 · Q65
The angle of elevation of a cloud from a point 200 m above a lake is 30° and the angle of depression of its reflection in the lake is 60°. The height of the cloud is
Elementary MathematicsTrigonometry
- A200 m
- B200 m
- C400 m
- D600 m
Explanation
Let the cloud be H above the lake, point 200 m above the lake, horizontal distance d: (H−200)/d = tan30°, (H+200)/d = tan60°. Dividing: (H+200)/(H−200) = tan60°/tan30° = 3, so H + 200 = 3H − 600 and H = 400 m (option C).