Abc has three sudes wuth these lengths: ab = 9, bc = 40, and ca = 41. what us the value of cos c

< C is opposite side  AB 
so applying the Cosine Rule:-

AB^2 = BC^2 + CA^2 -  2.BC.CA cos C

9^2 = 40^2 + 41^2 - 2.40.41 cos C

cos C  =  9^2 - 40^2 - 41^2
              = 0.97561
                   -2.40.41

m < C =  12.68 degrees