1. **Problem a:** Calculate the length of side $x$ in a triangle with angles 44° and 38°, and the side adjacent to the 44° angle is 10 units. 2. **Step 1:** Identify the third angle using the triangle angle sum rule: $$44^\circ + 38^\circ + \text{third angle} = 180^\circ$$ $$\text{third angle} = 180^\circ - 44^\circ - 38^\circ = 98^\circ$$ 3. **Step 2:** Use the Law of Sines: $$\frac{x}{\sin(44^\circ)} = \frac{10}{\sin(98^\circ)}$$ 4. **Step 3:** Solve for $x$: $$x = \frac{10 \times \sin(44^\circ)}{\sin(98^\circ)}$$ 5. **Step 4:** Calculate the sine values: $$\sin(44^\circ) \approx 0.6947, \quad \sin(98^\circ) \approx 0.9903$$ 6. **Step 5:** Substitute and simplify: $$x = \frac{10 \times 0.6947}{0.9903}$$ $$x = \frac{\cancel{10} \times 0.6947}{\cancel{0.9903}}$$ 7. **Step 6:** Calculate the value: $$x \approx 7.0$$ --- 1. **Problem b:** Calculate the height of a mast given a cable anchored 20 metres from the base and an angle of elevation of 68°. 2. **Step 1:** Draw a right triangle with the cable as the hypotenuse, the height of the mast as the opposite side, and the 20 metres as the adjacent side. 3. **Step 2:** Use the tangent function: $$\tan(68^\circ) = \frac{\text{height}}{20}$$ 4. **Step 3:** Solve for height: $$\text{height} = 20 \times \tan(68^\circ)$$ 5. **Step 4:** Calculate $\tan(68^\circ)$: $$\tan(68^\circ) \approx 2.4751$$ 6. **Step 5:** Substitute and calculate: $$\text{height} = 20 \times 2.4751 = 49.5$$ 7. **Step 6:** Round to the nearest metre: $$\text{height} \approx 50$$ **Final answers:** - a) $x \approx 7.0$ - b) Height of mast $\approx 50$ metres