Answer:
134.3
Step-by-step explanation:
In [tex]\triangle{WXZ},[/tex] a right triangle, look at sides XW and XZ.
[tex]\frac{XW}{XZ}=\frac{\text{adjacent}}{\text{hypotenuse}}=\cos{82^\circ}\\\\XW=(XZ)\cos{82^\circ}[/tex]
You now need to find XW.
In [tex]\triangle{XYZ},[/tex] the measure of angle XZY (the one at the top) is 180 - (82 + 67) = 31 degrees.
Using the Law of Sines in triangle XYZ,
[tex]\frac{XZ}{\sin{67^\circ}}=\frac{540}{\sin{31^\circ}}\\\\XZ=\frac{540 \sin{67^\circ}}{\sin{31^\circ}}[/tex]
Put that into the equation for XW above...
[tex]XW=\frac{540\sin{67^\circ}\cos{82^\circ}}{\sin{31^\circ}}[/tex]
A calculator shows that this is approximately 134.3
