In general, the law of cosines states that
[tex]\begin{gathered} c^2=a^2+b^2-2ab\cos C \\ a,b,c\rightarrow\text{ sides of a triangle} \\ C\rightarrow\text{ opposite angle to side c} \end{gathered}[/tex]
Thus, in our case,
[tex]\begin{gathered} AB^2=BC^2+CA^2-2*BC*CA\cos(37.4\degree) \\ \Rightarrow AB^2=2.45^2+3.16^2-2*2.45*3.16\cos(37.4\degree) \\ \Rightarrow AB^2=3.68738... \\ \Rightarrow AB\approx1.92 \end{gathered}[/tex]
Therefore, the answer is 1.92mi
