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\[(8^{2}+B^{2}+2*8*B*Cos40)=20^{2}\]
Can you proceed from here finding the value of B?

He is using the Law of cosines I mentioned above.

i think the preferred solution is Resultant = \[sqrt{A^2 + B^2}\]

But this is true if and only if vectors A and B are at right angles.

You should end up with B = 13.20