1. The problem asks for the value of $\tan 45^\circ$.\n\n2. Recall the definition of tangent in a right triangle: $\tan \theta = \frac{\text{opposite}}{\text{adjacent}}$.\n\n3. For special angles, the tangent values are well-known. Specifically, $\tan 45^\circ = 1$ because in a 45-45-90 triangle, the legs are equal, so opposite and adjacent sides are equal.\n\n4. Therefore, $\tan 45^\circ = 1$.\n\n5. Comparing with the options, the correct answer is b. 1.