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NDA 2019
Exam
NDA
Year
2019
Subject
Mathematics
Chapter
Heights and Distances

NDA 2019 · Mathematics · Heights and Distances

The angle of elevation of a tower of height h from a point A due...

The angle of elevation of a tower of height hh from a point A due South of it is x and from a point B due East of A is y. If AB=z\mathrm{AB}=\mathrm{z}, then which one of the following is correct ?

Options

  1. Ah2(cot⁡2y−cot⁡2x)=z2\mathrm{h}^2\left(\cot ^2 y-\cot ^2 x\right)=z^2
  2. Bz2(cot⁡2y−cot⁡2x)=h2z^2\left(\cot ^2 y-\cot ^2 x\right)=h^2
  3. Ch2(tan⁡2y−tan⁡2x)=z2\mathrm{h}^2\left(\tan ^2 \mathrm{y}-\tan ^2 \mathrm{x}\right)=\mathrm{z}^2
  4. Dz2(tan⁡2y−tan⁡2x)=h2z^2\left(\tan ^2 y-\tan ^2 x\right)=h^2

Correct answer

A. h2(cot⁡2y−cot⁡2x)=z2\mathrm{h}^2\left(\cot ^2 y-\cot ^2 x\right)=z^2

Step-by-step solution



from figure (iii), h2cot⁡2y=z2+h2cot⁡2x⇒z2=h2\mathrm{h}^2 \cot ^2 y=\mathrm{z}^2+\mathrm{h}^2 \cot ^2 \mathrm{x}\Rightarrow \mathrm{z}^2=\mathrm{h}^2\left(\cot ^2 \mathrm{y}-\cot ^2 \mathrm{x}\right)
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