1. **State the problem:** We are given a triangle with side $a=27$, angle $A=102^\circ$, angle $B=28^\circ$, and side $b$ opposite angle $B$. We need to find $b$ using the Law of Sines and round to the nearest tenth. 2. **Recall the Law of Sines formula:** $$\frac{a}{\sin A} = \frac{b}{\sin B}$$ This means the ratio of a side length to the sine of its opposite angle is the same for all sides of a triangle. 3. **Rearrange the formula to solve for $b$:** $$b = a \times \frac{\sin B}{\sin A}$$ 4. **Calculate the sines of the angles:** $$\sin 102^\circ \approx 0.9781$$ $$\sin 28^\circ \approx 0.4695$$ 5. **Substitute the known values:** $$b = 27 \times \frac{0.4695}{0.9781}$$ 6. **Simplify the fraction:** $$\frac{0.4695}{0.9781} \approx 0.4799$$ 7. **Calculate $b$:** $$b = 27 \times 0.4799 = 12.9573$$ 8. **Round to the nearest tenth:** $$b \approx 13.0$$ **Final answer:** $$b = 13.0$$