What is PC equal to?
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. H\text{ metres}
- B. \sqrt{2}H\text{ metres}
- C. \sqrt{3}H\text{ metres}
- D. 2H\text{ metres} ✓
Correct Answer: D. 2H\text{ metres}
Explanation
In the right-angled triangle formed by point P, cloud C, and horizontal line from P, the vertical opposite side is H and the angle of elevation is 30^\circ. Using trigonometry: \sin 30^\circ = \frac{H}{PC} \implies \frac{1}{2} = \frac{H}{PC} \implies PC = 2H.
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