How 9 Cheenta students ranked in top 100 in ISI and CMI Entrances?
Learn More

Direction & Angles | PRMO-2019 | Problem 4

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


Co-ordinate geometry


Check the Answer


PRMO-2018, Problem 13

Pre College Mathematics

Try with Hints

Direction & Angles - figure

According to the problem we draw the figure and try to solve using co-ordinate method...

Can you now finish the problem ..........

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........

Therefore distance covered =\(4 \times 9\)=\(36\)

Subscribe to Cheenta at Youtube

Knowledge Partner

Cheenta is a knowledge partner of Aditya Birla Education Academy

Cheenta Academy

Aditya Birla Education Academy

Aditya Birla Education Academy

Cheenta. Passion for Mathematics

Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.