1. **State the problem:** Find the cosine of angle $F$ in right triangle $FDE$ where $\angle D$ is the right angle. 2. **Recall the cosine definition:** For an angle in a right triangle, $\cos(\theta) = \frac{\text{adjacent side}}{\text{hypotenuse}}$. 3. **Identify sides relative to $\angle F$:** - Adjacent side to $\angle F$ is $FD = 8$. - Hypotenuse is $FE = 17$. 4. **Apply the formula:** $$\cos(F) = \frac{FD}{FE} = \frac{8}{17}$$ 5. **Simplify the fraction:** $\frac{8}{17}$ is already in simplest form. **Final answer:** $$\cos(F) = \frac{8}{17}$$