Answer
$$19.87^\circ $$
Work Step by Step
$$\eqalign{
& a = {\text{86}}.{\text{14 in}}.,b = {\text{253}}.{\text{2 in}}.,c = {\text{241}}.{\text{9 in}} \cr
& \cr
& {\text{Find }}A,{\text{ use the law of cosines}} \cr
& {a^2} = {b^2} + {c^2} - 2bc\cos A \cr
& \cos A = \frac{{{b^2} + {c^2} - {a^2}}}{{2bc}} \cr
& \cr
& {\text{Substitute}} \cr
& \cos A = \frac{{{{\left( {{\text{253}}.{\text{2}}} \right)}^2} + {{\left( {{\text{241}}.{\text{9}}} \right)}^2} - {{\left( {{\text{86}}.{\text{14}}} \right)}^2}}}{{2\left( {{\text{253}}.{\text{2}}} \right)\left( {{\text{241}}.{\text{9}}} \right)}} \cr
& {\text{Use a calculator}} \cr
& \cos A \approx 0.9404692315 \cr
& {\text{Use the inverse cosine function}} \cr
& A \approx {\cos ^{ - 1}}\left( {0.9404692315} \right) \cr
& A \approx 19.87^\circ \cr} $$
