Option B: $\dfrac{3}{4}$
Given $\cos A = \dfrac{4}{5}$, so adjacent side = 4, hypotenuse = 5. By Pythagoras theorem, opposite side = $\sqrt{25-16} = 3$. Therefore, $\tan A = \dfrac{3}{4}$.
Use the Pythagoras theorem to find the missing side, then apply $\tan A = \dfrac{\text{opposite}}{\text{adjacent}}$. Here, hypotenuse = 5, adjacent = 4, so opposite = 3, giving $\tan A = \tfrac{3}{4}$. A common mistake is confusing opposite and adjacent sides.