The Nearsighted Cow Problem

Question

A rectangular billboard 9 feet in height stands in a field so that its bottom is 12 feet above the ground. A nearsighted cow with eye level at 4 feet above the ground stands x ft from the billboard. Express θ, the vertical angle subtended by the billboard at her eye, in terms of x. Then find the distance  the cow x₀ must stand from the billboard to maximize θ.

θ(x)=

θ is maximized when x₀ =

the image describes this question is in the link(I can't post an image here and I don't know why): https://d2vlcm61l7u1fs.cloudfront.net/media%2Fe6e%2Fe6ef43ff-5f94-4caf-860d-06b2fcb1df5b%2Fphpx79BUN.png

Answer 1

There's only vertical measurments. Without an angle; I'm lost.

Bottom triangle:

a^2+b^2=c^2

x^2+8^2=c^2

α=acos((b^s+c^2-a^2)/(2bc))

" "((64+ " -x^2)/(16c))=θ

The picture's not to scale.