[tex]\sin \angle F~~= \dfrac{\text{Perpendicular}}{\text{Hypotenuse}}\\\\~~~~~~~~~~~~=\dfrac{GE}{EF}\\\\~~~~~~~~~~~~=\dfrac 2 3\\\\\implies \angle F=\sin^{-1} \left(\dfrac 23} \right)=41.8^{\circ}\\\\\text{Hence the measure of angle F is}~ 41.8^{\circ}[/tex]
