Let y be the shadow over neighbor's yard.
By similar triangles: x/(36+x2)1/2=(x+y)/15.
y'=(((15*(36+x2)1/2)-(15x2*(36+x2)-1/2)) / 36+x2) - 1.
Then set y'=0 and solve for x.
Finally subsitute x in the similar triangles formula to solve for y.
Michael Shackleford, A.S.A.