1. **Problem Statement:** We need to find the sine of angle $T$ in a right triangle where the side opposite $T$ is 20 units, the hypotenuse is 52 units, and the adjacent side is 48 units. 2. **Formula:** The sine of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse: $$\sin(T) = \frac{\text{opposite}}{\text{hypotenuse}}$$ 3. **Apply the values:** Here, the opposite side to angle $T$ is 20 and the hypotenuse is 52, so: $$\sin(T) = \frac{20}{52}$$ 4. **Simplify the fraction:** Both numerator and denominator can be divided by 4: $$\sin(T) = \frac{20 \div 4}{52 \div 4} = \frac{5}{13}$$ 5. **Final answer:** The sine of angle $T$ is: $$\sin(T) = \frac{5}{13}$$ This fraction is already in simplest form.