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NDA 2018
Exam
NDA
Year
2018
Subject
Mathematics
Chapter
Heights and Distances

NDA 2018 · Mathematics · Heights and Distances

If a flag-staff of 6 m height placed on the top of a tower throws a...

If a flag-staff of 6 m height placed on the top of a tower throws a shadow of 23m2 \sqrt{3} \mathrm{ m} along the ground, then what is the angle that the sun makes with the ground?

Options

  1. A60∘60^{{}^{\circ}}
  2. B45∘45^{{}^{\circ}}
  3. C30∘30^{{}^{\circ}}
  4. D15∘15^{{}^{\circ}}

Correct answer

A. 60∘60^{{}^{\circ}}

Step-by-step solution

A Bisthetower.is the tower.B Cis flag staff. The angles made by the shadows of towerandflagstaffaresame.tower and flag staff are same. In △ABE,tan⁡θ=hx...(1) In △ACD,tan⁡θ=h+6x+23...(2) from (1), (2), hx=h+6x+23⇒hx+23h=hx+6x⇒hx=623=33=3⋅33=3\begin{aligned} & \text{ In } \triangle A B E, \tan \theta=\frac{h}{x}...(1) \\ & \text{ In } \triangle A C D, \tan \theta=\frac{h+6}{x+2 \sqrt{3}}...(2)\\ & \text{ from (1), (2), } \frac{h}{x}=\frac{h+6}{x+2 \sqrt{3}} \Rightarrow h x+2 \sqrt{3} h=h x+6 x \\ & \Rightarrow \frac{h}{x}=\frac{6}{2 \sqrt{3}}=\frac{3}{\sqrt{3}}=\frac{\sqrt{3} \cdot \sqrt{3}}{\sqrt{3}}=\sqrt{3} \end{aligned}$from(1),from(1),\tan \theta=\frac{\mathrm{h}}{\mathrm{x}}=\sqrt{3} \Rightarrow \theta=60^{{}^{\circ}}$.
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