Question

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?​

Answer 1

Answer:

36 feet

Step-by-step explanation:

An ant leaves the anthill for its morning exercise

It walks 4feet East and then makes a 160 degree turn to the right and walks 4 more feet . It then makes another 160 degree turn to the right and walks 4 feet more

let say ant do such n turns to reach at same point

then turn taken in n steps = 160n deg

when ant will be back at same point angle should be multiple of 360°

=> 160n = 360 k

dividing by 40 both sides

=>  4n = 9k

=> n = 9  & k = 4 will satisfy

after 9 turns ant will be back to ant hill

Distance covered = 4*9 = 36 feet