Calculus Problem: Applied Optimization

Question

A rectangular billboard 5 feet in height stands in a field so that its bottom is 7 feet above the ground. A nearsighted cow with eye level at 4 feet above the ground stands  feet from the billboard. Express , the vertical angle subtended by the billboard at her eye, in terms of . Then find the distance  the cow must stand from the billboard to maximize .

Answer 1

a=1, b=eye to billboard base, c=eye to billboard bottom edge

a^2+b^2=c^2