What percentage of the field can the goat eat (assuming it can and will eat all grass in reach and knows no fear)?
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The answer is 39.1%.
It is complicated, and requires a diagram. Basically, the circles overlap with a sector of 120 degrees. You can find the sector area. If you double the sector area, you have to subtract 2 equilateral triangles from this area to get the area of edible grass. Divide by area of the circle to get fraction of total grass that the goat can eat. I really wish I had a pencil and paper on here!
It is complicated, and requires a diagram. Basically, the circles overlap with a sector of 120 degrees. You can find the sector area. If you double the sector area, you have to subtract 2 equilateral triangles from this area to get the area of edible grass. Divide by area of the circle to get fraction of total grass that the goat can eat. I really wish I had a pencil and paper on here!
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100%