1 + 1 = 2 (Need to draw, Part 6)

If you draw the path, you get an isoceles triangle with lengths 1. The angle is 45 degrees, since he waddled northwest. We can find the other two angles simply: $180-45=135$ , $\frac {135}{2}=67.5$ . We can solve suing the law of sines: $\frac {sin (45)}{x}=\frac {sin (67.5)}{1}$ . $x=\frac{sin (45)}{sin (67.5)}\approx 0.765$ . $\sqrt {2-\sqrt {2}}\approx 0.765$ .