Answer
$B = 114.66^\circ \hspace{10pt} A =63.16^\circ \hspace{10pt} a = 806.068\,m$
$B' = 114.66^\circ \hspace{10pt} A' = 13.84^\circ \hspace{10pt} a' = 216.101 \, m$
Work Step by Step
$\sin{B} = \dfrac{b \sin{C}}{c} = \dfrac{821 \sin{(51.5^\circ)}}{707}$
$\sin{B} = 0.908$
$B = 65.34^\circ\hspace{40pt} B' = 114.66^\circ$
$A = 180-(B+C) = 63.16^\circ$
$a = \dfrac{c \sin{A}}{\sin{C}} = \dfrac{707 \times \sin{63.16}}{\sin{51.5}}$
$a = 806.068 \,m$
$B' + C < 180 \hspace{10pt} \therefore B'$ is valid.
$A' = 180-(B+C') = 13.84^\circ$
$a' = \dfrac{c \sin{A'}}{\sin{C}} = \dfrac{707 \times \sin{13.84}}{\sin{51.5}}$
$a' = 216.101 \, m$