Answer
$$13{\text{m}}$$
Work Step by Step
$$\eqalign{
& {\text{From the triangle we can set:}} \cr
& C = 82^\circ ,\,\,\,B = 68^\circ ,\,\,\,a = 7.0{\text{ m,}}\,\,\,\,b = x? \cr
& \cr
& {\text{Calculate }}A \cr
& A = {180^ \circ } - B - C \cr
& A = {180^ \circ } - 68^\circ - 82^\circ \cr
& A = 30^\circ \cr
& \cr
& {\text{Calculate the side }}b{\text{ using the law of sines}} \cr
& \frac{b}{{\sin B}} = \frac{a}{{\sin A}} \cr
& b = \frac{{a\sin B}}{{\sin C}} \cr
& b = \frac{{7.0\sin \left( {68^\circ } \right)}}{{\sin \left( {30^\circ } \right)}} \cr
& b \approx 12.98{\text{m}} \cr
& \cr
& {\text{Therefore,}} \cr
& x = 13{\text{m}} \cr} $$
