What is the value of \theta?
The angle of elevation of a cloud at C from a point (P), H metres above the surface of a lake is 30^\circ. The height of the cloud from the surface of the lake is 2H metres. Let \theta be the angle of depression of the reflection of the cloud in the lake from the point P.
- A. 30^\circ
- B. 45^\circ
- C. 60^\circ ✓
- D. Cannot be determined due to insufficient data
Correct Answer: C. 60^\circ
Explanation
The vertical height of the cloud from P is 2H - H = H. The horizontal distance x satisfies \tan 30^\circ = \frac{H}{x} \implies x = H\sqrt{3}. The reflection of the cloud is 2H below the lake surface, making it 2H + H = 3H below P. Thus, \tan \theta = \frac{3H}{H\sqrt{3}} = \sqrt{3}, giving \theta = 60^\circ.
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