Question

Please ehlp delta math with explanation please

Answer 1

134.3

Explanation:

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

`(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,

`(XZ)/(sin(67^\circ))=(540)/(sin(31^\circ))\\\\XZ=(540 sin(67^\circ))/(sin(31^\circ))`

Put that into the equation for XW above...

`XW=(540sin(67^\circ)cos(82^\circ))/(sin(31^\circ))`

A calculator shows that this is approximately 134.3