A robot, which is initially facing North, is programmed to travel 5m then turn through $10^{\circ}$, travel 5m then turn through $20^{\circ}$, travel 5m then turn through $30^{\circ}$, and so on. Each move consists of moving 5m in a straight line and then turning clockwise through an angle which increases by $10^{\circ}$ at each move.

How far has it travelled by the time it is first facing due East at the end of a move?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.
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