Step 1 :Given a right triangle with side lengths adjacent to $\theta$ as 16 and opposite to $\theta$ as 13.
Step 2 :Use the tangent function to find the angle $\theta$: $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{13}{16}$
Step 3 :Find the angle $\theta$ using the inverse tangent function: $\theta = \arctan\left(\frac{13}{16}\right)$
Step 4 :Calculate the angle $\theta$ in radians: $\theta \approx 0.682$ radians
Step 5 :\(\boxed{\theta \approx 0.682 \text{ radians}}\)