Answer
$$19{\text{ cm}}$$
Work Step by Step
$$\eqalign{
& A = {\text{6}}0^\circ ,b = {\text{5}}.0{\text{ cm}},c = {\text{21 cm}} \cr
& \cr
& {\text{Find }}a,{\text{ use the law of cosines}} \cr
& {a^2} = {b^2} + {c^2} - 2bc\cos A \cr
& {a^2} = {\left( {{\text{5}}.0} \right)^2} + {\left( {{\text{21}}} \right)^2} - 2\left( {{\text{5}}.0} \right)\left( {{\text{21}}} \right)\cos \left( {{\text{6}}0^\circ } \right) \cr
& {\text{Use a calculator}} \cr
& {a^2} = 361 \cr
& {\text{Take square roots and choose the positive root}} \cr
& a = 19{\text{ cm}} \cr} $$
