3. Solve the triangle $A B C$ with the given information. Round each answer to the nearest tenth. $B=95.6^{\circ}, a=9.8, c=7.8$

Step 1 ：We are given two sides and an included angle of a triangle. We can use the Law of Cosines to find the third side. The Law of Cosines states that for any triangle with sides of lengths a, b, and c, and an angle γ opposite side c, the following relationship holds: \(c² = a² + b² - 2ab\cos(γ)\).

Step 2 ：In this case, we know a, c, and B (which is the angle opposite side b), so we can rearrange the formula to solve for b: \(b² = a² + c² - 2ac\cos(B)\).

Step 3 ：After finding b, we can use the Law of Sines to find the other two angles. The Law of Sines states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle. So, we can write: \(a/\sin(A) = b/\sin(B) = c/\sin(C)\).

Step 4 ：We can solve for A using the known values of a, b, and B: \(\sin(A) = a\sin(B)/b\).

Step 5 ：And similarly for C: \(\sin(C) = c\sin(B)/b\).

Step 6 ：Substituting the given values, we get: B = 95.6, a = 9.8, c = 7.8, b = 13.1, A = 48.1, C = 36.3.

Step 7 ：Final Answer: The solution to the triangle $ABC$ is $A = 48.1^{\circ}$, $B = 95.6^{\circ}$, $C = 36.3^{\circ}$, $a = 9.8$, $b = 13.1$, and $c = 7.8$. So, \(\boxed{A = 48.1^{\circ}, B = 95.6^{\circ}, C = 36.3^{\circ}, a = 9.8, b = 13.1, c = 7.8}\).