1. **State the problem:** We need to find the tangent of angle $B$ in a right triangle with sides $AC=16$, $CB=12$, and hypotenuse $AB=20$. 2. **Recall the definition of tangent:** For an angle in a right triangle, $\tan(\theta) = \frac{\text{opposite side}}{\text{adjacent side}}$. 3. **Identify sides relative to angle $B$:** - Opposite side to $B$ is $AC = 16$. - Adjacent side to $B$ is $CB = 12$. 4. **Calculate $\tan(B)$:** $$\tan(B) = \frac{AC}{CB} = \frac{16}{12}$$ 5. **Simplify the fraction:** $$\frac{16}{12} = \frac{4 \times 4}{4 \times 3} = \frac{4}{3}$$ 6. **Final answer:** $$\tan(B) = \frac{4}{3}$$ This is the simplified improper fraction for the tangent of angle $B$.