Dr. Bos' Problem:

Separating the Sheep

Aliens have landed and painted a large, 1-acre right triangle in the middle of Farmer Brown's field. It's magenta. The farmer puts posts in the midpoint of each side. He then tethers a sheep to each of the side posts and a goat to the post on the hypotenuse (in case the aliens come back). The ropes are just long enough to let each animal reach the two adjacent vertices. What is the total area the two sheep have to themselves, ie, the area the goat can't reach?

Due Friday, December 1^st at Noon.