2. Solve the triangle $A B C$ with the given information. Round each answer to the nearest tenth. $\quad A=35^{\circ}, b=7.8, c=5.6$

Step 1 ：Given that $A = 35.0^{\circ}$, $b = 7.8$, and $c = 5.6$ in triangle $ABC$.

Step 2 ：Use the Law of Sines to find angle $B$: $\frac{b}{\sin A} = \frac{c}{\sin B}$.

Step 3 ：Solve for $B$ to get $B = 24.3^{\circ}$.

Step 4 ：Find angle $C$ by subtracting the sum of angles $A$ and $B$ from $180^{\circ}$: $C = 180^{\circ} - A - B$.

Step 5 ：Solve for $C$ to get $C = 120.7^{\circ}$.

Step 6 ：Use the Law of Sines again to find side $a$: $\frac{a}{\sin A} = \frac{b}{\sin B}$.

Step 7 ：Solve for $a$ to get $a = 10.9$.

Step 8 ：\(\boxed{A = 35.0^{\circ}, B = 24.3^{\circ}, C = 120.7^{\circ}, a = 10.9, b = 7.8, c = 5.6}\)