Direction & Angles | PRMO-2019 | Problem 4

Contents

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:\(36\)

Source

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 =\(4 \times 9\)=\(36\)

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?