Calculate the cosine of an angle in a right triangle given side lengths.

1. Identify the problem type: The problem asks for the cosine of an angle in a right triangle, which is a trigonometry problem.
2. Recall the definition of cosine: In a right triangle, the cosine of an angle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse. Mathematically, $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$.
3. Identify the angle of interest: The problem asks for $\cos(\angle E)$.
4. Identify the sides of the triangle relative to angle E: In the given right triangle $\triangle FDE$, angle D is the right angle ($90^\circ$).
- The side adjacent to angle E is the side DE, which has a length of 8.
- The hypotenuse is the side opposite the right angle, which is FE, with a length of 17.
- The side opposite angle E is FD, with a length of 15.
5. Apply the cosine definition: Using the definition of cosine, we can write:
$$\cos(\angle E) = \frac{\text{length of side DE}}{\text{length of side FE}}$$
6. Substitute the given values: Substitute the lengths of the adjacent side (DE = 8) and the hypotenuse (FE = 17) into the formula:
$$\cos(\angle E) = \frac{8}{17}$$
7. State the final answer: The value of $\cos(\angle E)$ is $\frac{8}{17}$.