A trigonometry question

Let $y$ be the width of the rectangle and $x$ be its length. We know that $x=4y$. Using the pythagorean theorem, the length of the diogonal $z$ is 
\[z=\sqrt{x^2+y^2}=\sqrt{(4y)^2+y^2}=\sqrt{17y^2}=\sqrt{17}y.\]
Cosine equals adjacent over hypotenuse, which is
\[\cos (\theta)=\frac{x}{z}=\frac{4y}{\sqrt{17}y}=\frac{4}{\sqrt{17}}.\]