2022 · Q46
Consider the following for the next two (02) items that follow: From a point P located H metres above the surface of a lake, the angle of elevation of a cloud C is 30°. Let A be the point on the horizontal line through P such that CA is vertical and CA = H metres. The reflection of the cloud in the lake is observed from P at an angle of depression θ. What is the value of θ?
Elementary MathematicsTrigonometry
- A30°
- B45°
- C60°
- DCannot be determined due to insufficient data
Explanation
The cloud is H metres above P's level (2H above the lake); with angle of elevation 30°, the horizontal distance is H√3. Its mirror image is 3H below P's level, so tanθ = 3H/(H√3) = √3, giving θ = 60°. The keyed option is C.