A man starts from a point X and walks 20 metres to reach a point Y in the north-east direction. He then turns right and walks 20 metres again to reach a point Z. How far is point Z from point X?

Point Z is 20 root 2 metres from X.

XY = 20 m along north-east.

A right turn from a north-east heading points to south-east, and YZ = 20 m.

North-east and south-east directions are perpendicular, so angle XYZ = 90 degrees.

XZ = root(20 x 20 + 20 x 20) = root(800) = 20 root 2.

Method: Pythagoras on the two perpendicular legs.