Sonia cycles 20 km towards the East. From there she cycles 8 km towards the West, and then 5 km towards the North. How far and in which direction is she from her starting point?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 13 km North-East
Keep a running total of the distance east (or west) and north (or south) of the start; when both are left over, the straight distance is the hypotenuse of a right triangle.
20 km East: 20 km east of the start
8 km West: \(20-8=12\) km east
5 km North: 12 km east, 5 km north
Distance \(=\sqrt{12^{2}+5^{2}}=\sqrt{169}=13\) km
She is north and east of the start, so the direction is North-East
She is 13 km North-East of her starting point.
