1. **State the problem:** We have a right triangle with a hypotenuse of length 28, one acute angle of 45°, and we need to find the length of the side adjacent to the 45° angle, labeled as $x$. 2. **Recall the relevant formula:** In a right triangle, the side adjacent to an angle $\theta$ can be found using the cosine function: $$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$$ 3. **Apply the formula:** Here, $\theta = 45^\circ$, hypotenuse = 28, and adjacent side = $x$. $$\cos(45^\circ) = \frac{x}{28}$$ 4. **Solve for $x$:** $$x = 28 \times \cos(45^\circ)$$ 5. **Calculate $\cos(45^\circ)$:** $$\cos(45^\circ) = \frac{\sqrt{2}}{2} \approx 0.7071$$ 6. **Substitute and compute:** $$x = 28 \times 0.7071 = 19.7988$$ 7. **Round to two decimal places:** $$x \approx 19.80$$ **Final answer:** $x = 19.80$ which corresponds to option C.