Answer:
Area of the triangle WXY = 111.8 mm²
Step-by-step explanation:
By applying Sine rule in the given triangle WXY,
[tex]\frac{\text{SinW}}{\text{XY}}=\frac{\text{SinX}}{\text{WY}}=\frac{\text{SinY}}{\text{WX}}[/tex]
Since m∠W + m∠X + m∠Y = 180°
m∠W + 26° + 130° = 180°
m∠W = 180° - 156°
m∠W = 24°
[tex]\frac{\text{Sin24}}{\text{XY}}=\frac{\text{Sin130}}{31}=\frac{\text{Sin26}}{\text{WX}}[/tex]
[tex]\frac{\text{Sin24}}{\text{XY}}=\frac{\text{Sin130}}{31}[/tex]
XY = [tex]\frac{31\times (\text{Sin24})}{\text{Sin130}}[/tex]
XY = 16.4597
≈ 16.4597 mm
Area of the triangle = [tex]\frac{1}{2}(\text{XY})(\text{WY})\text{SinY}[/tex]
= [tex]\frac{1}{2}(16.4597)(31)\text{Sin26}[/tex]
= 111.83 mm²
≈ 111.8 mm²
Therefore, area of the triangle WXY = 111.8 mm²
