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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

But try the problem first…

Answer:$36$

Source

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 =$4 \times 9$=$36$