1. The problem: Find the length $x$ in the right-angled triangle where the hypotenuse is 16 cm and one angle is 24° 2. In a right triangle, the side opposite an angle can be found by multiplying the hypotenuse by the sine of the angle. This is because $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$. 3. Here, the side $x$ is opposite the 24° angle, and the hypotenuse is 16 cm, so: $$x = 16 \times \sin(24^\circ)$$ 4. Calculate $\sin(24^\circ)$ (using a calculator or sine table): $$\sin(24^\circ) \approx 0.4067$$ 5. Multiply to find $x$: $$x = 16 \times 0.4067 = 6.5072$$ 6. Therefore, the length $x$ is approximately 6.51 cm. **Final answer:** $x \approx 6.51$ cm.