a 41 b 8 c 73 c2 a2 b2 2 ab cos C C2 a2 b2 2ab cos

a = 4.1 b = 8 c = 7.3 c^2 = a^2 + b^2 - 2 ab cos C C^2 = a^2 + b^2 - 2ab cos C (7.3)^2 = (9.1)^2 + (8)^2 - 2(4.1)(8) cos C 2(9.1)(8)cosC = (4.1)^2 + (8)^2 - (7.3)^2 cosC = 4.1^2 + 8^2 - 7.3^2/2(4.1)(8) cos C = 27.52/65.6 C = 65.2 but this is what Im getting

Solution

a= 4.1   ,   b= 8    ,    c=7.3

a²=b²+c²-2ac cos A

4.1²= 8² +   7.3² - 2(8)(7.3) cos A

116.8 cos A= 100.48

cos A= 100.48/116.8= 30.7 degree

using sine law

sinA/a=sinB/b

sin 30.7/4.1= sin B/8

sinB= 8 sin 30.65/4.1

B=84.1 degree

C=180-A-B=65.2 degree

With those data,your answer is absolutely correct