Try this beautiful Geometry problem from PRMO, 2019 based on Direction & Angles.
Direction & Angles | PRMO | Problem-4
An ant leaves the anthill for its morning exercise. It walks 4 feet east and then makes a 160° turn to the right and walks 4 more feet. It then makes another 160° turn to the right and walks 4 more feet. If the ant continues this pattern until it reaches the anthill again, what is the distance in feet it would have walked?
- $20$
- $36$
- $13$
Key Concepts
Geometry
Co-ordinate geometry
Trigonometry
Check the Answer
But try the problem first…
Answer:\(36\)
PRMO-2018, Problem 13
Pre College Mathematics
Try with Hints
First hint
According to the problem we draw the figure and try to solve using co-ordinate method…
Can you now finish the problem ……….
Second Hint
Let \(A_0(0,0)\)
Therefore \(A_1(4 cos 0,4sin 0)\)
\(A_2(4cos 0+4 cos 160, 4 sin 0+4 sin 160)\)
\(\Rightarrow A_n =(0,0)\)
and \(4(cos 0+cos 160 +…+sin 160(n-1)=0\)
\(\Rightarrow n =9\)
Can you finish the problem……..
Final Step
Therefore distance covered =\(4 \times 9\)=\(36\)
Other useful links
- https://www.cheenta.com/problem-based-on-triangle-prmo-2012-problem-7/
- https://www.youtube.com/watch?v=TRf4TgrOIpA
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