1. **State the problem:** We need to find the length of side $g$ in triangle $GEF$ where angles and some sides are given. 2. **Given:** - Angle $G = 38^\circ$ - Angle $E = 107^\circ$ - Side $GE = 13$ - Side $EF = g$ (unknown) - Side $GF = e$ (not needed for this problem) 3. **Find the missing angle $F$:** $$F = 180^\circ - G - E = 180^\circ - 38^\circ - 107^\circ = 35^\circ$$ 4. **Use the Law of Sines:** $$\frac{g}{\sin G} = \frac{GE}{\sin F}$$ 5. **Substitute known values:** $$\frac{g}{\sin 38^\circ} = \frac{13}{\sin 35^\circ}$$ 6. **Solve for $g$:** $$g = \frac{13 \times \sin 38^\circ}{\sin 35^\circ}$$ 7. **Calculate sine values:** $$\sin 38^\circ \approx 0.6157, \quad \sin 35^\circ \approx 0.5740$$ 8. **Evaluate $g$:** $$g = \frac{13 \times 0.6157}{0.5740} \approx \frac{8.0041}{0.5740} \approx 13.94$$ 9. **Round to nearest tenth:** $$g \approx 13.9$$ **Final answer:** $$\boxed{13.9}$$