1. **Problem:** Find the value of $x$ in a right triangle where the side adjacent to the angle $48^\circ$ is 21 cm, and $x$ is the side opposite the $48^\circ$ angle. 2. **Formula:** Use the sine ratio: $$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$$ or cosine ratio if adjacent and opposite sides are involved. Here, since we have adjacent side and want opposite side, use tangent or sine with hypotenuse if known. But since hypotenuse is unknown, use tangent: $$\tan(48^\circ) = \frac{x}{21}$$ 3. **Calculation:** $$x = 21 \times \tan(48^\circ)$$ 4. **Evaluate:** $$x = 21 \times 1.1106 = 23.3226$$ 5. **Round to 3 significant figures:** $$x = 23.3$$ cm **Answer:** $x = 23.3$ cm This is the first question solved as requested.