A boy runs 4 km to the east side, then turns right and runs 6 km, then again turns left and runs 8 km, then again turns left to run 3 km and finally again turns left to run 4 km. Now the boy is looking in which direction, and the distance of the final point from the starting point is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → West, \(\sqrt{73}\)
Each turn is taken from the direction the boy is facing at that moment:
Runs 4 km facing East
Facing East, a right turn is South: runs 6 km
Facing South, a left turn is East: runs 8 km
Facing East, a left turn is North: runs 3 km
Facing North, a left turn is West: runs 4 km, and he is still facing West at the end
The distance from the start is the hypotenuse of a right triangle whose sides are the net East and net South movements:
Net East: \(4+8-4=8\) km
Net South: \(6-3=3\) km
Distance \(=\sqrt{8^2+3^2}=\sqrt{64+9}=\sqrt{73}\) km