**Step 1 — Interpret the given ratio in a right triangle.**
$$\cos A = \frac{\text{base}}{\text{hypotenuse}} = \frac{4}{5}$$
So base $= 4k$, hypotenuse $= 5k$.

**Step 2 — Find the perpendicular using Pythagoras theorem.**
$$\text{perp.} = \sqrt{(5k)^2 - (4k)^2} = \sqrt{25k^2 - 16k^2} = \sqrt{9k^2} = 3k$$

**Step 3 — Compute $\tan A$.**
$$\tan A = \frac{\text{perpendicular}}{\text{base}} = \frac{3k}{4k} = \frac{3}{4}$$

**Answer : (B) $\dfrac{3}{4}$**