1. **Problem statement:** Find the missing side $x$ in the right-angled triangle with a side of 3 cm and an angle of 33° opposite to $x$. 2. **Formula and rules:** In a right triangle, the sine of an angle is the ratio of the length of the opposite side to the hypotenuse: $$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$$ 3. **Identify sides:** Here, $x$ is opposite the 33° angle, and the hypotenuse is 3 cm. 4. **Apply the formula:** $$\sin(33^\circ) = \frac{x}{3}$$ 5. **Solve for $x$:** $$x = 3 \times \sin(33^\circ)$$ 6. **Calculate:** Using a calculator, $$\sin(33^\circ) \approx 0.5446$$ 7. **Final value:** $$x = 3 \times 0.5446 = 1.6338$$ 8. **Answer rounded to 1 decimal place:** $x = 1.6$ cm This matches the given answer $1.63$ cm to 2 decimal places.