1. **Problem Statement:** Find $\cos(\beta)$ in a right triangle where the side opposite to angle $\beta$ is 3, the side adjacent to $\beta$ is 4, and the hypotenuse is 5. 2. **Formula:** The cosine of an angle in a right triangle is defined as the ratio of the length of the adjacent side to the hypotenuse: $$\cos(\beta) = \frac{\text{adjacent side}}{\text{hypotenuse}}$$ 3. **Apply the values:** Here, the adjacent side to $\beta$ is 4 and the hypotenuse is 5, so: $$\cos(\beta) = \frac{4}{5}$$ 4. **Interpretation:** This means the cosine of angle $\beta$ is $\frac{4}{5}$, which corresponds to option C. **Final answer:** $\cos(\beta) = \frac{4}{5}$ (Option C)