1. **State the problem:** We need to find the measure of angle $\angle B$ in a right triangle where side $AC=22$, side $BC=18$, and angle $C$ is $90^\circ$. 2. **Recall the trigonometric formula:** In a right triangle, the tangent of an angle is the ratio of the opposite side to the adjacent side. For angle $B$, the opposite side is $AC=22$ and the adjacent side is $BC=18$. 3. **Write the formula:** $$\tan(\angle B) = \frac{\text{opposite}}{\text{adjacent}} = \frac{22}{18}$$ 4. **Calculate the ratio:** $$\frac{22}{18} = \frac{\cancel{22}}{\cancel{18}} = 1.2222...$$ 5. **Find the angle using inverse tangent:** $$\angle B = \tan^{-1}(1.2222...)$$ 6. **Use a calculator to find the angle:** $$\angle B \approx 50.2^\circ$$ 7. **Round to the nearest tenth:** The measure of $\angle B$ is approximately $50.2^\circ$. **Final answer:** $$m\angle B \approx 50.2^\circ$$