#### Answer

$\cos(B)=\frac{4}{5}$

#### Work Step by Step

The cosine of an angle in a right triangle is the ratio of the adjacent side to the hypotenuse. The side adjacent to $B$ has a measure of $8$, and the hypotenuse has a measure of $10$. When we write these in a ratio, we get $\frac{8}{10}$, which simplifies to $\frac{4}{5}$.