Correct. Use the definition of sine together with the given information to find e:

$\displaystyle\frac{{e}}{{15}}=\frac{{3}}{{5}}\Rightarrow{5}{e}={45}\Rightarrow{e}={9}\usepackage{cmbright}\Huge\$

Now use the Pythagorean Theorem to find d, the length of $\displaystyle{\overline{{{F}{E}}}}\usepackage{cmbright}\Huge\$ :

$\displaystyle{{9}}^{{2}}+{{d}}^{{2}}={{15}}^{{2}}\Rightarrow{81}+{{d}}^{{2}}={225}\Rightarrow{{d}}^{{2}}={144}\Rightarrow{d}={12}\usepackage{cmbright}\Huge\$