A cyclist rides 5 km north, turns right and rides 2 km, turns left and rides 7 km, then turns right and rides 3 km. How far is the cyclist from the starting point?

Explanation

1. 01

   Headings: north, east, north, east.

2. 02

   Total north $= 5 + 7 = 12$ km; total east $= 2 + 3 = 5$ km.

3. 03

   Distance $= \sqrt{12^2 + 5^2} = \sqrt{169} = 13$ km.