Correct. Use the definition of tangent together with the given information to find u:

$\displaystyle\frac{{u}}{{30}}=\frac{{8}}{{15}}\Rightarrow{15}{u}={240}\Rightarrow{u}={16}\usepackage{cmbright}\Huge\$

Now use the Pythagorean Theorem to find the hypotenuse w:

$\displaystyle{{w}}^{{2}}={{30}}^{{2}}+{{16}}^{{2}}\Rightarrow{{w}}^{{2}}={900}+{256}\Rightarrow{{w}}^{{2}}={1156}\Rightarrow{w}={34}\usepackage{cmbright}\Huge\$