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

NDA 2018 · Mathematics · Heights and Distances

The top of a hill observed from the top and bottom of a building of...

The top of a hill observed from the top and bottom of a building of height h is at angles of elevation π6\frac{\pi}{6} and π3\frac{\pi}{3} respectively. What is the height of the hill?

Options

  1. A2h
  2. B3h/2
  3. Ch
  4. Dh/2

Correct answer

B. 3h/2

Step-by-step solution


From question, In △PQR\triangle \mathrm{PQR} and △PST\triangle \mathrm{PST}. B=Htan⁡π3=H−htan⁡π6⇒H3=H−h⇒23H=h⇒H=32h\begin{aligned} & \mathrm{B}=\frac{\mathrm{H}}{\tan \frac{\pi}{3}}=\frac{\mathrm{H}-h}{\tan \frac{\pi}{6}} \\ \Rightarrow \quad & \frac{\mathrm{H}}{3}=\mathrm{H}-h \\ \Rightarrow & \frac{2}{3} \mathrm{H}=h \\ \Rightarrow & \mathrm{H}=\frac{3}{2} h \end{aligned}
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