Try this beautiful Geometry problem from PRMO, 2019 based on Direction & Angles.
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?
Geometry
Co-ordinate geometry
Trigonometry
But try the problem first...
Answer:\(36\)
PRMO-2018, Problem 13
Pre College Mathematics
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 =\(4 \times 9\)=\(36\)
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