Answer
$$84.4{\text{ }}{{\text{m}}^2}$$
Work Step by Step
$$\eqalign{
& A = {\text{59}}.{\text{8}}0^\circ ,b = {\text{15}}.00{\text{ m}},\,\,C = {\text{53}}.{\text{1}}0^\circ \cr
& {\text{Find the angle }}B \cr
& B = 180^\circ - A - C \cr
& B = 180^\circ - {\text{59}}.{\text{8}}0^\circ - {\text{53}}.{\text{1}}0^\circ \cr
& B = 67.1^\circ \cr
& \cr
& {\text{Use the law of sines to find side }}a \cr
& \frac{a}{{\sin A}} = \frac{b}{{\sin B}} \cr
& a = \frac{{b\sin A}}{{\sin B}} \cr
& a = \frac{{15.00{\text{m}}\sin \left( {{\text{59}}.{\text{8}}0^\circ } \right)}}{{\sin \left( {67.1^\circ } \right)}} \cr
& a \approx 14.073{\text{ m}} \cr
& \cr
& {\text{Find the area of the triangle using the formula }}Area = \frac{1}{2}ab\sin C \cr
& Area = \frac{1}{2}\left( {14.073{\text{ m}}} \right)\left( {{\text{15}}.00{\text{ m}}} \right)\sin \left( {{\text{53}}.{\text{1}}0^\circ } \right) \cr
& Area \approx 84.4{\text{ }}{{\text{m}}^2} \cr} $$
