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COMEDK · Maths · 18. Heights and Distances

From an aeroplane flying, vertically above a horizontal road, the angles of depression of two consecutive stones on the same side of the aeroplane are observed to be \(30^{\circ}\) and \(60^{\circ}\) respectively. The height at which the aeroplane is flying in \(\mathrm{km}\), is

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

Answer & Solution

Correct Answer

(C) \(\frac{\sqrt{3}}{2}\)

Step-by-step Solution

Detailed explanation

Let the distance of two consecutive stones are \((x, x+1)\). In \(\triangle B C D\), we have \(\tan 60^{\circ}=\frac{h}{x}\) \(\Rightarrow \quad x=\frac{h}{\sqrt{3}}...(i)\) In \(\triangle A B C\), we have \(\tan 30^{\circ}=\frac{h}{x+1}\)…