1. **Problem a:** Calculate the length of side $x$ in a triangle with angles 38° and 44°, and side 10 opposite the 38° angle. 2. Use the Law of Sines formula: $$\frac{a}{\sin A} = \frac{b}{\sin B}$$ where $a$ and $b$ are sides opposite angles $A$ and $B$ respectively. 3. Here, $a=10$, $A=38^\circ$, $B=44^\circ$, and $b=x$. 4. Substitute values: $$\frac{10}{\sin 38^\circ} = \frac{x}{\sin 44^\circ}$$ 5. Solve for $x$: $$x = \frac{10 \times \sin 44^\circ}{\sin 38^\circ}$$ 6. Calculate sines: $\sin 38^\circ \approx 0.6157$, $\sin 44^\circ \approx 0.6947$. 7. Substitute: $$x = \frac{10 \times 0.6947}{0.6157}$$ 8. Simplify fraction: $$x = 10 \times \frac{0.6947}{0.6157} = 10 \times 1.128 = 11.28$$ 9. Round to one decimal place: $x = 11.3$. 10. **Problem b:** Calculate the height of a mast given a cable anchored 20 m from the base and angle of elevation 68°. 11. Use right triangle trigonometry: height $h = 20 \times \tan 68^\circ$. 12. Calculate $\tan 68^\circ \approx 2.4751$. 13. Compute height: $$h = 20 \times 2.4751 = 49.502$$ 14. Round to nearest metre: $h = 50$ metres.