Question 3
Initially, a robot faces north. Whenever it stops moving, it automatically faces north. It is programmed to do the following:
(1) Turn $30^\circ$ to the right, move $1$ km forward and stop.
(2) Turn $90^\circ$ to the right, move $1$ km forward and stop.
(3) Turn $150^\circ$ to the right, move $1$ km forward and stop.
(4) Turn $210^\circ$ to the right, move $1$ km forward and stop.
(5) Turn $270^\circ$ to the right, move $1$ km forward and stop.
(6) Turn $330^\circ$ to the right, move $1$ km forward and stop.
What is the distance between the initial and final positions of the robot?
(1) Turn $30^\circ$ to the right, move $1$ km forward and stop.
(2) Turn $90^\circ$ to the right, move $1$ km forward and stop.
(3) Turn $150^\circ$ to the right, move $1$ km forward and stop.
(4) Turn $210^\circ$ to the right, move $1$ km forward and stop.
(5) Turn $270^\circ$ to the right, move $1$ km forward and stop.
(6) Turn $330^\circ$ to the right, move $1$ km forward and stop.
What is the distance between the initial and final positions of the robot?