Let y be the shadow over neighbor's yard.

By similar triangles: x/(36+x^{2})^{1/2}=(x+y)/15.

y=15x/(36+x^{2})^{1/2}-x.

y^{'}=(((15*(36+x^{2})^{1/2})-(15x^{2}*(36+x^{2})^{-1/2}))
/ 36+x^{2}) - 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.