Answer
$\approx 3.43 $
Work Step by Step
From the law of cosines
$6^{2}=4^{2}+x^{2}-2\times 4\times x\times \cos 110\Rightarrow x^{2}-x\times \left( 8\cos 110\right) +\left( 4^{2}-6^{2}\right) =0$
$x^{2}-8\cos 110\times x-20=0\Rightarrow x=\dfrac {8\cos 110\pm \sqrt {\left( 8\cos 110\right) ^{2}+4\times 20}}{2}\approx \dfrac {8\times \left( -0.342\right) \pm \sqrt {\left( 8\times \left( -0.342\right) \right) ^{2}+80}}{2} \approx 3.43$
