A cyclist goes 12 km to the South and then turning West he goes 16 km. Again he turns to his right and goes 15 km. After that, he turns to his right and goes 12 km. How far is he from his starting point?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 5 km
Each turn is taken from the direction the cyclist is facing at that moment:
He goes South 12 km, then turns West and goes 16 km
Facing West, a right turn is North: he goes 15 km
Facing North, a right turn is East: he goes 12 km
Where he ends:
North-South: 12 km South, then 15 km North, so he ends 3 km North of the start
East-West: 16 km West, then 12 km East, so he ends 4 km West of the start
The distance from the start (these two distances are at right angles, so by Pythagoras):
Distance \(=\sqrt{3^2+4^2}=\sqrt{25}=5\) km