1. **State the problem:** We need to find the cosine of angle $T$ in right triangle $TUV$ where $TU=20$, $UV=48$, and hypotenuse $TV=52$. 2. **Recall the cosine definition:** In a right triangle, $\cos(\theta) = \frac{\text{adjacent side}}{\text{hypotenuse}}$. 3. **Identify the sides relative to angle $T$:** The side adjacent to angle $T$ is $TU=20$, and the hypotenuse is $TV=52$. 4. **Apply the formula:** $$\cos(T) = \frac{TU}{TV} = \frac{20}{52}$$ 5. **Simplify the fraction:** $$\frac{20}{52} = \frac{\cancel{4} \times 5}{\cancel{4} \times 13} = \frac{5}{13}$$ 6. **Final answer:** $$\cos(T) = \frac{5}{13}$$