1. **State the problem:** We need to find the cosine of angle $C$ in a right triangle where the hypotenuse is 45 and the side adjacent to angle $C$ is 28. 2. **Recall the cosine definition:** For a right triangle, $\cos(\theta) = \frac{\text{adjacent side}}{\text{hypotenuse}}$. 3. **Apply the formula:** $$\cos(C) = \frac{28}{45}$$ 4. **Simplify the fraction if possible:** 28 and 45 have no common factors other than 1, so the fraction is already in simplest form. 5. **Final answer:** $$\cos(C) = \frac{28}{45}$$ This means the cosine of angle $C$ is $\frac{28}{45}$, which is approximately 0.6222.