2017 JJC P1 Q10
A laser from a fixed point $O$ on a flat ground projects light beams to the top of two vertical structures $A$ and $B$ as shown above. To project the beam to the top of $A$, the laser makes an angle of elevation of $\frac{\pi }{6}$ radians. To project the beam to the top of $B$, the laser makes an angle of elevation of $\left( \frac{\pi }{6}+x \right)$ radians. The two structures $A$ and $B$ are of heights $h$ m and $\left( h+\sqrt{3}k \right)$m respectively and are $10$m and $\left( 10+k \right)$m away from $O$ respectively.
(i)
Show that the length of the straight beam from $O$ to $A$ is $\frac{20}{\sqrt{3}}$m.
[1]
(ii)
Show that the length of $AB$ is $2k$m and that the angle of elevation of $B$ from $A$ is $\frac{\pi }{3}$ radians.
[3]
(iii)
Hence, using the sine rule, show that $k=\frac{10\sin x}{\sqrt{3}\sin \left( \frac{\pi }{6}-x \right)}$.
[2]
(iv)
If $x$ is sufficiently small, show that $k\approx \frac{20}{\sqrt{3}}\left( x+a{{x}^{2}} \right)$, where $a$ is a constant to be determined.
[6]
Suggested Video Solutions
Share with your friends!
Continue reading
5 Exam Preparation Tips: How We Help Students Excel in Exams
In the ever-evolving landscape of education, where academic success is often measured by performance in exams, the need for effective test preparation has never been more critical. Students face a
List MF 27
What is the MF 27? The MF 27, set to replace the MF 26 from 2025, is a comprehensive formula sheet developed by the Ministry of Education Singapore in collaboration
Panic No More: What To Do The Day Before An Exam?
As you approach the final hours before your exam, remember that a balanced approach is key. A light review can keep the information fresh in your mind, while preparing your