Triangles FIM and LAK below are similar, with $\displaystyle{m}\angle{F}={m}\angle{L}\usepackage{cmbright}\Huge\$ and $\displaystyle{m}\angle{M}={m}\angle{K}\usepackage{cmbright}\Huge\$ .

What is the length of $\displaystyle{\overline{{{L}{A}}}}\usepackage{cmbright}\Huge\$ ?