Answer
$$15.826{\text{ ft}}$$
Work Step by Step
$$\eqalign{
& {\text{From the triangle we can set:}} \cr
& C = 70.3^\circ ,\,\,\,b = 12.2{\text{ ft}},\,\,\,a = 15.0{\text{ ft,}}\,\,\,\,c = ? \cr
& \cr
& {\text{Use the Law of cosines to find }}c \cr
& {c^2} = {a^2} + {b^2} - 2ab\cos C \cr
& {\text{Substitute}} \cr
& {c^2} = {\left( {15.0} \right)^2} + {\left( {12.2} \right)^2} - 2\left( {15.0} \right)\left( {12.2} \right)\cos \left( {70.3^\circ } \right) \cr
& {\text{Use a calculator}} \cr
& {c^2} = 250.4631354 \cr
& {\text{Take square roots and choose the positive root}} \cr
& c \approx 15.826{\text{ ft}} \cr} $$
