Arectangular billboard 5 feet in height stands in a field so that its bottom is 6 feet above the ground. a nearsighted cow with eye level at 4 feet above the ground stands x feet from the billboard. express θ, the vertical angle subtended by the billboard at her eye, in terms of x. then find the distance x0 the cow must stand from the billboard to maximize θ.

In order to maximize , the cow must stand 3.74 ft away from the billboard, approximately.

Explanation:

The vertical angle subtended by the billboard at the cow's eye can be calculated from

Now, maximaxing , we have

Solving the equation for

Which can be interpretated as the cow standing either one or the other side from the billboard. The next plot confirms that 's positive root, gives a maximum for the angle .

because growing process had stoped after 4-5 year