1. **Problem Statement:** Find the secant of angle $X$ in the right triangle $XVW$ where $XV=8$, $VW=15$, and hypotenuse $XW=17$. 2. **Recall the definition:** Secant of an angle in a right triangle is the reciprocal of cosine. $$\sec(X) = \frac{1}{\cos(X)}$$ 3. **Cosine formula:** $$\cos(X) = \frac{\text{adjacent side to } X}{\text{hypotenuse}}$$ Here, the side adjacent to angle $X$ is $XV=8$, and the hypotenuse is $XW=17$. 4. **Calculate cosine:** $$\cos(X) = \frac{8}{17}$$ 5. **Calculate secant:** $$\sec(X) = \frac{1}{\cos(X)} = \frac{1}{\frac{8}{17}}$$ 6. **Simplify the fraction:** $$\sec(X) = \frac{1}{\frac{8}{17}} = \frac{1 \times 17}{8} = \frac{17}{8}$$ 7. **Final answer:** $$\boxed{\sec(X) = \frac{17}{8}}$$