It appears that you correctly used the Pythagorean Theorem to find the length of the hypotenuse. However, you have found the value of $\displaystyle{\sin{{X}}}\usepackage{cmbright}\Huge\$ . Remember that:

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

The correct answer is $\displaystyle\frac{{3}}{\sqrt{{34}}}\usepackage{cmbright}\Huge\$ .