To find the length of AB, we have to se law of cosine, which is
[tex] AB^2 = AC^2 + BC^2 -2(AC)(BC) cos C [/tex]
Substituting the given values of AC, BC and angle C
[tex] AB^2 = 6^2 + 7^2 -2(6)(7) cos 83
\\
AB^2 = 36+49 - 84 cos 83 [/tex]
[tex] AB^2 = 74.763
[/tex]
Taking square root on both sides
[tex] AB = 8.6 [/tex]
Therefore the correct option is the third option .
