Solve the following math problem step by step. The last line of your response should be of the form Answer: \boxed{$Answer} where $Answer is the answer to the problem.

<image> The diagonals of rectangle $A B C D$ each have a length of 56 feet. If $m \angle B A C=42^{\circ}$, what is the length of $\overline{A B}$ to the nearest tenth of a foot?