You found the value of $\displaystyle{\cos{{E}}}\usepackage{cmbright}\Huge\$ . First use the Pythagorean Theorem to find e:

$\displaystyle{{e}}^{{2}}+{{4}}^{{2}}={{9}}^{{2}}\usepackage{cmbright}\Huge\$

After solving for e, use the definition of cotangent:

$\displaystyle\text{cotangent}=\frac{\text{adjacent}}{\text{hypotenuse}}\usepackage{cmbright}\Huge\$

The correct answer is $\displaystyle\frac{{4}}{\sqrt{{65}}}\usepackage{cmbright}\Huge\$ .