1. **Problem statement:** Find the unknown side $x$ in triangle e) with sides 6.553 cm, 4 cm, and $x$, and angles 30°, 25°, and 125°. 2. **Formula:** Use the sine rule for sides: $$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$$ where $a,b,c$ are sides opposite angles $A,B,C$ respectively. 3. **Identify known values:** - Side opposite 30° is 6.553 cm - Side opposite 25° is 4 cm - Side opposite 125° is $x$ 4. **Apply sine rule to find $x$:** $$\frac{x}{\sin 125^\circ} = \frac{6.553}{\sin 30^\circ}$$ 5. **Rearrange to solve for $x$:** $$x = \frac{6.553}{\sin 30^\circ} \times \sin 125^\circ$$ 6. **Calculate values:** - $\sin 30^\circ = 0.5$ - $\sin 125^\circ = \sin (180^\circ - 125^\circ) = \sin 55^\circ \approx 0.8192$ 7. **Substitute and compute:** $$x = \frac{6.553}{0.5} \times 0.8192 = 13.106 \times 0.8192 = 10.74$$ 8. **Final answer:** The length of side $x$ is approximately **10.7 cm** (to 3 significant figures).