Question 22494
Draw the equilateral triangle.
Each angle is 60 degrees or 1/6 th of a circle.
The area of a complete circle is (pi)(radius)^2
You want your goat to eat a swath that is (1/6)(pi)(r^2)
and for that swath to equal (1/2)[2(3.14)]
Equation:
     (1/6)(pi)(r^2)= (1/2)[2(3.14)]
3.14 is approximately equal to pi so divide both sides by pi
     (1/6)r^2 = (1/2)(2)
          r^2 = 6
          r  = sqrt6 =2.44 ft.

Cheers,
Stan H.