text: Agree with HayHarbr, but in this case, we can use \n\n1) the relation between central angle and inscribed angle (central angle = 2 * inscribed angle)\n\n2) the trigonmetric formual for the area of a triangle\n(S(ABC) = [b*c*sin(A)]/2)\n\nEquation I: Area of the crescent = half area of the field\n[R1^2 * Alpha/2] - [R2^2 * Alpha/4] - [R1^2 * sin(Alpha)]/2 + [R2^2 * sin(Alpha/2)]/2 = pi/2 * R1^2\n\nEquation II: \nR1 * sin(Alpha/2) = R2 * sin(Alpha/4)\n\nWhere\nR1 = radius of the field\nR2 = length of the rope\n\nAbove system of 2 equations is sovable for R2 against R1. As HayHarbr said, it can take a long time to solve manually!\n\nFurther comments:\n\n1) If things do not simplify, we shall get a solution with reverse trigonometric function (ArcSin).\n\n2) What about the approximation \nR2 = SQRT[R1^2 + (R1^2)/4 + (R1^2)/16]\nR1 = radius of the field\nR2 = length of the rope\n\n3) Hope you allow considering that the field is FLAT, neglecting also the sphericity of the Earth. If not, I surrender.\n\n4) Finally, we are lucky to have a round field. Think how is the shape of the fields of our neighbors and how they should solve the same problem for them.