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NDA 2015
Exam
NDA
Year
2015
Subject
Mathematics
Chapter
Heights and Distances

NDA 2015 · Mathematics · Heights and Distances

The angle of elevation of the top of a tower from a point 20 m away...

The angle of elevation of the top of a tower from a point 20 mm away from its base is 45∘45^{{}^{\circ}}. What is the height of the tower?

Options

  1. A10 m
  2. B20 m
  3. C30 m
  4. D40 m

Correct answer

B. 20 m

Step-by-step solution

In △ABC,\triangle \mathrm{ABC},AB=hBC=20m∠C=45∘\begin{aligned} & \mathrm{AB}=\mathrm{h} \\ & \mathrm{BC}=20 \mathrm{ m} \\ & \angle \mathrm{C}=45^{{}^{\circ}} \end{aligned}∴tan⁡45∘=ABBC1=h20[∵tan⁡45∘=1]\therefore \quad \tan 45^{{}^{\circ}}=\frac{\mathrm{AB}}{\mathrm{BC}}1=\frac{\mathrm{h}}{20} \quad\left[\because \tan 45^{{}^{\circ}}=1\right]h=20m∴ Height of the tower =20m∴ Option (B) is correct. \begin{array}{ll} & \mathrm{h}=20 \mathrm{ m} \\ \therefore & \text{ Height of the tower }=20 \mathrm{ m} \\ \therefore \quad & \text{ Option (B) is correct. }\end{array}$$
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