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triangular field

A one hectare field is in the shape of a right angled triangle. At the midpoint of each side is a post. Horace the goat is tethered at the midpoint of the hypotenuse, and two sheep, Sid and Sadie, at the midpoints of the other two sides. Each rope is just exactly long enough to allow the animal to reach two adjacent vertices. One and only one animal can reach all points in the field. Which one is it and why?