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TS EAMCET · Maths · Heights and Distances

From the top of a hill \(h\) metres high the angles of depressions of the top and the bottom of a pillar are \(\alpha\) and \(\beta\) respectively. The height (in metres) of the pillar is

  1. A \(\frac{h(\tan \beta-\tan \alpha)}{\tan \beta}\)
  2. B \(\frac{h(\tan \alpha-\tan \beta)}{\tan \alpha}\)
  3. C \(\frac{h(\tan \beta+\tan \alpha)}{\tan \beta}\)
  4. D \(\frac{h(\tan \beta+\tan \alpha)}{\tan \alpha}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{h(\tan \beta-\tan \alpha)}{\tan \beta}\)

Step-by-step Solution

Detailed explanation

Let \(A B\) be a hill whose height is \(h\) metres and \(C D\) be a pillar of height \(h^{\prime}\) metres. In \(\triangle E D B\), \(\tan \alpha=\frac{h-h^{\prime}}{E D}\) and in \(\triangle A C B\), \(\tan \beta=\frac{h}{A C}=\frac{h}{E D}\) Eliminate \(E D\) from Eqs. (i) and…