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