Question

find wz and the area of △wxy. write your answer as an integer or as a decimal rounded to the nearest tenth. wz = cm area = cm²

Explanation:

Step1: Find WZ using sine - function

In right - triangle WYZ, $\sin Y=\frac{WZ}{WY}$. Given $WY = 15$ cm and $Y = 24^{\circ}$. So, $WZ=WY\times\sin Y$. Substituting the values, we have $WZ = 15\times\sin(24^{\circ})$. Since $\sin(24^{\circ})\approx0.4067$, then $WZ=15\times0.4067 = 6.1005\approx6.1$ cm.

Step2: Find the area of $\triangle WXY$

The base of $\triangle WXY$ is considered as $XY = 26$ cm and the height is $WZ\approx6.1$ cm. The area formula for a triangle is $A=\frac{1}{2}\times base\times height$. So, $A=\frac{1}{2}\times26\times6.1$. First, $26\times6.1 = 158.6$, then $\frac{1}{2}\times158.6=79.3$ $cm^{2}$.

Answer:

$WZ = 6.1$ cm
Area $= 79.3$ $cm^{2}$