If theta = (4)/(5) and theta is an acute angle, what is the value of theta?

Substitute the given value $\sin \theta = \frac{4}{5}$ into the identity.

$$\left(\frac{4}{5}\right)^2 + \cos^2 \theta = 1$$

$$\cos^2 \theta = 1 - \frac{16}{25}$$

To subtract, express 1 as $\frac{25}{25}$:

$$\cos^2 \theta = \frac{25}{25} - \frac{16}{25}$$ $$\cos^2 \theta = \frac{9}{25}$$

$$\cos \theta = \pm\sqrt{\frac{9}{25}}$$ $$\cos \theta = \pm\frac{3}{5}$$

Since $\theta$ is an acute angle, it lies in the first quadrant ($0^\circ < \theta < 90^\circ$). In the first quadrant, both sine and cosine values are positive.
Therefore, $\cos \theta$ must be positive.

$$\cos \theta = \frac{3}{5}$$

The value of $\cos \theta$ is $\boxed{\frac{3}{5}}$.