Answer:
[tex]7\sqrt{91}\ units[/tex] or [tex]66.78\ units[/tex]
Step-by-step explanation:
we know that
Applying the law of cosines
[tex]c^{2}=a^{2}+b^{2}-2abcos(C)[/tex]
In this problem we have
[tex]a=42\ units, b=35\ units, C=120\°[/tex]
c is the length of the third side
Substitute
[tex]c^{2}=42^{2}+35^{2}-2(42)(35)cos(120\°)[/tex]
[tex]c^{2}=1,764+1,225-2,940cos(120\°)[/tex]
[tex]c^{2}=4,459[/tex]
[tex]c=\sqrt{4,459}\ units[/tex]
[tex]c=7\sqrt{91}\ units[/tex] or [tex]c=66.78\ units[/tex]
