Answer:
Area of the triangle = 469.4 ft²
Step-by-step explanation:
By applying Sine rule in the given triangle WXY,
[tex]\frac{\text{SinW}}{\text{XY}}=\frac{\text{SInY}}{\text{WX}}=\frac{\text{SinX}}{\text{WY}}[/tex]
Since m∠X + m∠Y + m∠W = 180°
m∠X + 40° + 27° = 180°
m∠X = 180° - 67°
m∠X = 113°
Now substitute the measures of sides and angles given in the picture,
[tex]\frac{\text{Sin27}}{\text{XY}}=\frac{\text{SIn40}}{38}=\frac{\text{Sin113}}{\text{WY}}[/tex]
[tex]\frac{\text{Sin27}}{\text{XY}}=\frac{\text{SIn40}}{38}[/tex]
XY = [tex]\frac{38\text{(Sin27)}}{\text{Sin40}}[/tex]
XY = 26.84
Area of the triangle = [tex]\frac{1}{2}(\text{XY})(\text{XW})(\text{SinX})[/tex]
= [tex]\frac{1}{2}(26.84)(38)(\text{Sin113})[/tex]
= 469.42
≈ 469.4 ft²
