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

NDA 2019 · Mathematics · Heights and Distances

A ladder 9 m long reaches a point 9 m below the top of a vertical...

A ladder 9 m long reaches a point 9 m below the top of a vertical flagstaff. From the foot of the ladder, the elevation of the flagstaff is 60∘60^{{}^{\circ}}. What is the height of the flagstaff?

Options

  1. A9 m
  2. B10.5 m
  3. C13.5 m
  4. D15 m

Correct answer

C. 13.5 m

Step-by-step solution

△PAB\triangle P A B is isosceles △\triangle⇒θ=30∘ In △ABD\begin{aligned} & \Rightarrow \theta=30^{{}^{\circ}} \\ & \text{ In } \triangle A B D \end{aligned}$\begin{aligned} & \tan 30^{{}^{\circ}}=\frac{h}{x}=\frac{1}{\sqrt{3}} \\ & \Rightarrow x=h \sqrt{3} \end{aligned}\text{ In } \triangle P B O \text{, }tan⁡60∘=3=9+hx⇒3=9+hh3⇒3h=q+h⇒h=92m\begin{aligned} & \tan 60^{{}^{\circ}}=\sqrt{3}=\frac{9+h}{x} \\ & \Rightarrow \sqrt{3}=\frac{9+h}{h \sqrt{3}} \\ & \Rightarrow 3 h=q+h \\ & \Rightarrow h=\frac{9}{2} m \end{aligned}\thereforeTotalheightTotal height=13.5 \mathrm{ m}$
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