By the law of cosines, the angle [tex]C[/tex] satisfies
[tex]8.77^2=2^2+9^2-2\times2\times9\times\cos C[/tex]
which reduces to
[tex]\cos C=0.2246\implies C=\arccos(0.2246)\approx1.34422\text{ rad}[/tex]
which converts to approximately 77 degrees (this can be done my multiplying by 180 and dividing by pi).
