Answer
$${\text{10}}{\text{.63ft}}$$
Work Step by Step
$$\eqalign{
& {\text{From the triangle we set:}} \cr
& A = 22^\circ ,\,\,\,C = 115^\circ ,\,\,\,b = 8.0{\text{ ft,}}\,\,\,\,c = ? \cr
& \cr
& {\text{Calculate }}B \cr
& B = {180^ \circ } - A - C \cr
& B = {180^ \circ } - 22^\circ - 115^\circ \cr
& B = 43^\circ \cr
& \cr
& {\text{Calculate the side }}c{\text{ using the law of sines}} \cr
& \frac{c}{{\sin C}} = \frac{b}{{\sin B}} \cr
& c = \frac{{b\sin C}}{{\sin B}} \cr
& c = \frac{{8.0\sin \left( {115^\circ } \right)}}{{\sin \left( {43^\circ } \right)}} \cr
& c \approx 10.63{\text{ ft}} \cr
& \cr
& {\text{Thelength of the brace is 10}}{\text{.63ft}} \cr} $$
