Use the law of cosines to find the measure of angle YXZ.
[tex]8^2=6.5^2+6^2-2(6.5)(6)\cos(\angle YXZ)[/tex]
[tex]\cos(\angle YXZ)\approx0.1827[/tex]
[tex]\angle YXZ\approx 1.3871\text{ rad}\approx79.4734^\circ[/tex]
This means angles YXW and WXZ share the same measure of about [tex]39.7367^\circ[/tex].
Use the law of cosines again to find the measure of angle XZW.
[tex]6.5^2=8^2+6^2-2(8)(6)\cos(\angle XZW)[/tex]
[tex]\cos(\angle XZW)\approx0.6016[/tex]
[tex]\angle XZW\approx0.9253\text{ rad}\approx53.0181^\circ[/tex]
This means the measure of angle XWZ is
[tex]180^\circ=\angle WXZ+\angle XWZ+\angle XZW\implies \angle XWZ\approx87.25^\circ[/tex]
Now using the law of sines, you have
[tex]\dfrac{\sin(\angle WXZ)}{WZ}=\dfrac{\sin(\angle XWZ)}6\implies WZ\approx3.84[/tex]
