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