You found the value of $\displaystyle{\sin{{Y}}}\usepackage{cmbright}\Huge\$ . First use the Pythagorean Theorem to find x:

$\displaystyle{{5}}^{{2}}+{{x}}^{{2}}={{8}}^{{2}}\usepackage{cmbright}\Huge\$

After solving for x, use the definition of tangent:

$\displaystyle\text{tangent}=\frac{\text{opposite}}{\text{adjacent}}\usepackage{cmbright}\Huge\$