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TS EAMCET · Maths · Heights and Distances

The angle of elevation of a stationary cloud from a point \(2500 \mathrm{~m}\) above a lake is \(15^{\circ}\) and from the same point the angle of depression of its reflection in the lake is \(45^{\circ}\). The height (in metres) of the cloud above the lake, given that \(\cot 15^{\circ}=2+\sqrt{3}\), is

  1. A 2500
  2. B \(2500 \sqrt{2}\)
  3. C \(2500 \sqrt{3}\)
  4. D 5000
Verified Solution

Answer & Solution

Correct Answer

(C) \(2500 \sqrt{3}\)

Step-by-step Solution

Detailed explanation

In \(\triangle E C D\) \(\cot 15^{\circ}=\frac{E C}{C D}\) \(\begin{array}{ll}\Rightarrow & E C=C D \cot 15^{\circ} \\ \Rightarrow & E C=C D(2+\sqrt{3}), \text { given }\end{array}\) \(\Rightarrow \quad E C=(H-h)(2+\sqrt{3})\) ...(i) In…