Answer:
Area of the triangle WXY = 365.3 mm²
Step-by-step explanation:
By applying Sine rule in the given triangle XYW,
[tex]\frac{\text{SinY}}{\text{WX}}=\frac{\text{SinX}}{\text{YW}}[/tex]
[tex]\frac{\text{Sin70}}{\text{WX}}=\frac{\text{Sin43}}{\text{24}}[/tex]
WX = [tex]\frac{24.\text{Sin70}}{\text{Sin43}}[/tex]
= 33.068 mm
= 33.07 mm
Area of a triangle = [tex]\frac{1}{2}a.b.\text{Sin}\theta[/tex]
where a and b are the sides of the triangle and θ is the angle between the sides a and b.
Area = [tex]\frac{1}{2}(33.07)(24)\text{SinW}[/tex]
Since, m∠X + m∠Y + m∠W = 180°
m∠W = 180 - (43 + 70)
= 67°
Area of the triangle WXY = [tex]12\times (33.07)\text{Sin67}[/tex]
= 365.29 mm²
≈ 365.3mm²
