Answer:
[tex]a=4.1[/tex]
Step-by-step explanation:
The Law of Cosines is given as:
[tex]a^2=c^2+b^2-2cb\cos A[/tex].
Plugging in given values, we get:
[tex]a^2=4^2+2^2-2\cdot 4 \cdot 2\cos 78^{\circ},\\a^2=16+4-16\cos 78^{\circ},\\a^2\approx \sqrt{16.673},\\a\approx \fbox{$4.1$}[/tex].
