Question

find wz and the area of △xyz. write your answer as an integer or as a decimal rounded to the nearest tenth. wz = mi area = mi²

Explanation:

Step1: Find WZ using sine - function

In right - triangle WYZ, $\sin Y=\frac{WZ}{YZ}$. Given $YZ = 30$ mi and $Y=24^{\circ}$, we have $WZ=YZ\times\sin Y$.
$WZ = 30\times\sin(24^{\circ})$
$WZ=30\times0.406737\approx12.2$ mi

Step2: Find the area of $\triangle XYZ$

The area of a triangle is $A=\frac{1}{2}\times base\times height$. Here, the base is $XY = 46$ mi and the height is $WZ\approx12.2$ mi.
$A=\frac{1}{2}\times46\times12.2$
$A = 23\times12.2=280.6$ mi²

Answer:

$WZ\approx12.2$ mi
Area $\approx280.6$ mi²