The correct option is D. [tex]c^{2} =(42)^{2} +(35)^{2} -2(35)(42)cos120[/tex].
Given triangle has two sides of length 42 and 35, and angle between these two sides is 120°.
The Law of Cosines is used to find the remaining parts of an oblique (non-right) triangle when either the lengths of two sides and the measure of the included angle is known (S A S) or the lengths of the three sides (SSS) are known.
From this law ,we have [tex]a^{2} =b^{2} +c^{2} -2 bc cos \alpha[/tex] , here a is the length of side to be calculated and alpha is the angle between the known side.
So,here [tex]a^{2} =(42)^{2} +(35)^{2} -2(42)(35) cos120[/tex], since angle between the known sides is 120°.
Hence the correct option is D. [tex]c^{2} =(42)^{2} +(35)^{2} -2(35)(42)cos120[/tex].
For more details on Law of cosine follow the link:
https://brainly.com/question/17289163
