Using the law of cosines, it is found that the length of side AB is of AB = 13.
What is the law of cosines?
The law of cosines states that we can find the angle C of a triangle as follows:
[tex]c^2 = a^2 + b^2 - 2ab\cos{C}[/tex]
in which:
- c is the length of the side opposite to angle C.
- a and b are the lengths of the other sides.
For this problem, the parameters are:
C = 120, a = 8, b = 7.
Hence:
[tex]c^2 = a^2 + b^2 - 2ab\cos{C}[/tex]
[tex]c^2 = 8^2 + 7^2 - 2(8)(7)\cos{120^\circ}[/tex]
[tex]c^2 = 169[/tex]
[tex]c = \sqrt{169}[/tex]
c = 13.
Hence AB = 13.
More can be learned about the law of cosines at https://brainly.com/question/2491835
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