1. **Problem Statement:** Find the secant of angle $V$ in the right triangle $UVW$ where $\angle U$ is the right angle, $UW=48$, $UV=20$, and hypotenuse $VW=52$. 2. **Recall the definition:** The secant of an angle in a right triangle is the ratio of the hypotenuse to the adjacent side. 3. **Identify sides relative to $\angle V$:** - Hypotenuse: $VW = 52$ - Adjacent side to $\angle V$: $UV = 20$ 4. **Apply the formula:** $$\sec(V) = \frac{\text{hypotenuse}}{\text{adjacent}} = \frac{VW}{UV} = \frac{52}{20}$$ 5. **Simplify the fraction:** $$\frac{52}{20} = \frac{\cancel{52}^{26}}{\cancel{20}^{10}} = \frac{26}{10} = \frac{\cancel{26}^{13}}{\cancel{10}^{5}} = \frac{13}{5}$$ 6. **Final answer:** $$\sec(V) = \frac{13}{5}$$