1. **State the problem:** Convert $\sin 112^\circ$ into a trigonometric ratio of an acute angle using the identity $\sin(90^\circ + \theta) = \cos \theta$. 2. **Recall the identity:** The formula states that $\sin(90^\circ + \theta) = \cos \theta$. This means if we can write $112^\circ$ as $90^\circ + \theta$, then $\sin 112^\circ = \cos \theta$. 3. **Find $\theta$:** $$112^\circ = 90^\circ + \theta \implies \theta = 112^\circ - 90^\circ = 22^\circ$$ 4. **Apply the identity:** $$\sin 112^\circ = \sin(90^\circ + 22^\circ) = \cos 22^\circ$$ 5. **Conclusion:** The trigonometric ratio of the acute angle $22^\circ$ equivalent to $\sin 112^\circ$ is $\cos 22^\circ$. **Final answer:** $$\sin 112^\circ = \cos 22^\circ$$