Both Acute Angles

Once one acute angle is known, the other is free: the two share the 90° the right angle leaves, so the second is 90° minus the first. In a 3, 4, 5 triangle the angle opposite the 3 is arctan(3/4), about 36.87°, so the angle opposite the 4 is about 53.13°.

You can also find the second angle directly, reading the sides from it: the 4 is opposite $\theta$ and the 3 is adjacent, so $\theta = \arctan\left(\frac{4}{3}\right)$, again about 53.13°. Going direct does not lean on the first answer, so a slip there cannot carry over, and the two routes check each other.