1. **State the problem:** We need to find the measure of angle $\angle B$ in a right triangle with sides $AC=22$ and $BC=18$, where $\angle C$ is the right angle. 2. **Identify the sides relative to $\angle B$:** - Opposite side to $\angle B$ is $AC=22$. - Adjacent side to $\angle B$ is $BC=18$. 3. **Use the tangent function:** The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side: $$\tan(\angle B) = \frac{\text{opposite}}{\text{adjacent}} = \frac{22}{18}$$ 4. **Calculate the ratio:** $$\frac{22}{18} = \frac{\cancel{22}}{\cancel{18}} = \frac{11}{9} \approx 1.2222$$ 5. **Find the angle using the inverse tangent (arctan):** $$\angle B = \tan^{-1}(1.2222)$$ 6. **Calculate the angle in degrees:** Using a calculator, $$\angle B \approx 50.2^\circ$$ 7. **Final answer:** $$m\angle B \approx 50.2^\circ$$