Using the triangle sum theorem, we can conclude:
[tex]\begin{gathered} m\angle A+m\angle B+m\angle C=180 \\ 40+m\angle B+50=180 \\ so\colon \\ m\angle B=180-50-40 \\ m\angle B=180-90 \\ m\angle B=90 \end{gathered}[/tex]Now, we can use the law of sines in order to find AB:
[tex]\begin{gathered} \frac{AB}{\sin(C)}=\frac{AC}{\sin (B)} \\ solve_{\text{ }}for_{\text{ }}AB\colon_{} \\ AB=\frac{\sin (C)\cdot AC}{\sin (B)} \\ AB=\frac{\sin (50)\cdot100}{\sin (90)} \\ AB=76.60444431ft \end{gathered}[/tex]