1. **State the problem:** We have a right-angled triangle with one angle of 28 degrees and the side adjacent to this angle measuring 12 meters. We need to find the hypotenuse. 2. **Formula used:** In a right triangle, the cosine of an angle is the ratio of the adjacent side to the hypotenuse: $$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$$ 3. **Apply the formula:** Here, $\theta = 28^\circ$, adjacent side = 12 m, and hypotenuse = $h$. $$\cos(28^\circ) = \frac{12}{h}$$ 4. **Solve for $h$:** Multiply both sides by $h$ and then divide both sides by $\cos(28^\circ)$: $$h \times \cos(28^\circ) = 12$$ $$\cancel{h} = \frac{12}{\cos(28^\circ)}$$ 5. **Calculate the value:** Using a calculator, $$\cos(28^\circ) \approx 0.8829$$ $$h = \frac{12}{0.8829} \approx 13.59$$ 6. **Final answer:** The hypotenuse is approximately 13.59 meters.