7. $m \angle C=63^{\circ}, A B=28, A C=29$, find $m \angle B$.

Step 1 ：We are given a triangle with \(m \angle C=63^{\circ}\), \(AB=28\), and \(AC=29\).

Step 2 ：We can use the Law of Cosines to find the length of side BC. The Law of Cosines is \(c^2 = a^2 + b^2 - 2ab \cos C\).

Step 3 ：Substituting the given values into the formula, we get \(BC = \sqrt{28^2 + 29^2 - 2 \cdot 28 \cdot 29 \cdot \cos(63^{\circ})} \approx 29.79\).

Step 4 ：Next, we can use the Law of Sines to find the measure of angle B. The Law of Sines is \(\sin A/a = \sin B/b = \sin C/c\).

Step 5 ：Rearranging the formula to find \(m \angle B\), we get \(m \angle B = \sin^{-1}((\sin(63^{\circ}) \cdot 28) / 29.79) \approx 56.86^{\circ}\).

Step 6 ：Final Answer: The measure of angle B is approximately \(\boxed{56.86^{\circ}}\).