Answer:
The length of third side of the triangle is:
66.78 units.
Step-by-step explanation:
We are given one side of a triangle let 'a': 42 units.
Also the other side of the triangle let 'b': 35 units.
Also, the angle between the two sides let C=120 degree.
Also we know that the cosine rule to find the third side( let 'c') is given by:
[tex]c^2=a^2+b^2-2ab\cos C\\\\c^2=(42)^2+(35)^2-2\times 42\times 35\times \cos (120\degree)\\\\c^2=1764+1225+1470[/tex]
Since,
[tex]\cos (120)=\cos (90+30)\\\\\cos (120)=-\sin (30)\\\\\cos (120)=-\dfrac{1}{2}[/tex]
Hence,
[tex]c^2=4459\\\\c=\sqrt{4459}\\\\c=66.7757[/tex]
which is approximately equal to:
66.78 units.
Hence, length of third side of the triangle is:
66.78 units
