Answer:
The length of the third side of the triangle is [tex]7\sqrt{91}\ units[/tex]
Step-by-step explanation:
Let
c ----> the length of the third side of the triangle
we know that
Applying the law of cosines
[tex]c^2=a^2+b^2-2(a)(b)cos(C)[/tex]
we have
[tex]a=42\ units\\b=35\ units\\C=120^o[/tex]
substitute the given values
[tex]c^2=42^2+35^2-2(42)(35)cos(120^o)[/tex]
[tex]c^2=2,989-2,940cos(120^o)[/tex]
[tex]c^2=4,459\\c=\sqrt{4,459}\ units\\c=7\sqrt{91}\ units[/tex]
