From the given information, the sketch of the problem is shown below:
It is required to find the distance between points A and B.
The sum of angles in a triangle is 180º, it follows that:
[tex]\begin{gathered} A+B+C=180^{\circ} \\ \Rightarrow70.5^{\circ}+B+38.83^{\circ}=180^{\circ} \\ \Rightarrow B+109.33^{\circ}=180^{\circ} \\ \Rightarrow B=180^{\circ}-109.33^{\circ} \\ \Rightarrow B=70.67^{\circ} \end{gathered}[/tex]Recall from the Law of Sines that the following equation holds:
[tex]\frac{AB}{\sin C}=\frac{AC}{\sin B}[/tex]Substitute the angle measures and side length into the equation:
[tex][/tex]
