Question

Please ehlp delta math with explanation please

Answer 1

Answer:

134.3

Step-by-step explanation:

In $\triangle{WXZ},$ a right triangle, look at sides XW and XZ.

$\frac{XW}{XZ}=\frac{\text{adjacent}}{\text{hypotenuse}}=\cos{82^\circ}\\\\XW=(XZ)\cos{82^\circ}$

You now need to find XW.

In $\triangle{XYZ},$ the measure of angle XZY (the one at the top) is 180 - (82 + 67) = 31 degrees.

Using the Law of Sines in triangle XYZ,

$\frac{XZ}{\sin{67^\circ}}=\frac{540}{\sin{31^\circ}}\\\\XZ=\frac{540 \sin{67^\circ}}{\sin{31^\circ}}$

Put that into the equation for XW above...

$XW=\frac{540\sin{67^\circ}\cos{82^\circ}}{\sin{31^\circ}}$

A calculator shows that this is approximately 134.3