1. **Problem:** Given a triangle with angles 100° and 38°, and side opposite 100° is 13 cm, find side $x$ opposite 38°. 2. **Formula:** Use the Law of Sines: $$\frac{a}{\sin A} = \frac{b}{\sin B}$$ where $a,b$ are sides opposite angles $A,B$ respectively. 3. **Find the third angle:** $$180^\circ - 100^\circ - 38^\circ = 42^\circ$$ 4. **Apply Law of Sines:** Let side opposite 38° be $x$, side opposite 100° is 13 cm. $$\frac{x}{\sin 38^\circ} = \frac{13}{\sin 100^\circ}$$ 5. **Calculate $x$:** $$x = \frac{13 \times \sin 38^\circ}{\sin 100^\circ}$$ 6. **Evaluate sines:** $$\sin 38^\circ \approx 0.6157, \quad \sin 100^\circ \approx 0.9848$$ 7. **Compute:** $$x = \frac{13 \times 0.6157}{0.9848} \approx \frac{8.0041}{0.9848} \approx 8.13$$ 8. **Answer:** $x = 8.1$ cm (to 1 decimal place).