Given cos θ = 4/5, we can find tan θ using the identity tan θ = sin θ / cos θ. First, find sin θ using the Pythagorean identity: sin²θ + cos²θ = 1.

Substitute cos θ: sin²θ + (4/5)² = 1 → sin²θ + 16/25 = 1 → sin²θ = 1 - 16/25 = 9/25 → sin θ = 3/5 (taking positive root for acute angle).

Therefore, tan θ = sin θ / cos θ = (3/5) / (4/5) = 3/4.

Final answer: $\frac{3}{4}$