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TS EAMCET · Maths · Heights and Distances

A tower subtends angles \(\alpha, 2 \alpha\) and \(3 \alpha\) respectively at points \(A, B\) and \(C\), all lying on a horizontal line through the foot of the tower, then \(\frac{A B}{B C}\) is equal to:

  1. A \(\frac{\sin 3 \alpha}{\sin 2 \alpha}\)
  2. B \(1+2 \cos 2 \alpha\)
  3. C \(2 \cos 2 \alpha\)
  4. D \(\frac{\sin 2 \alpha}{\sin \alpha}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(1+2 \cos 2 \alpha\)

Step-by-step Solution

Detailed explanation

In \(\triangle E C D\), \(\tan 3 \alpha=\frac{h}{C D}\) \(\Rightarrow \quad C D=h \cot 3 \alpha \quad \ldots({i})\) In \(\triangle E B D\), \(\tan 2 \alpha=\frac{h}{B D}\) \(\Rightarrow \quad B D=h \cot 2 \alpha \quad \ldots({ii})\) In \(\triangle E A D\),…