A rectangular billboard 5 feet in height stands in a field so that its bottom is 8 feet above the ground. A nearsighted cow with eye level at 4 feet above the ground stands x feet from the billboard.

A rectangular billboard 5 feet in height stands in a field so that its bottom is 8 feet above the ground. A nearsighted cow with eye level at 4 feet above the ground stands x feet from the billboard. Express \theta, the vertical angle subtended by the billboard at her eye, in terms of x. Then find the distance x_{0} the cow must stand from the billboard to maximize \theta.