You may have used the definition of cotangent, but you incorrectly used the Pythagorean Theorem to find e. The correct equation is:

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

After solving this equation, substitute the value of e for the opposite side in the definition of cotangent. The correct answer is $\displaystyle\frac{{4}}{\sqrt{{65}}}\usepackage{cmbright}\Huge\$ .