Question

What the correct answer now

Answer 1

Answer:

Area of the triangle WXY = 111.8 mm²

Step-by-step explanation:

By applying Sine rule in the given triangle WXY,

$\frac{\text{SinW}}{\text{XY}}=\frac{\text{SinX}}{\text{WY}}=\frac{\text{SinY}}{\text{WX}}$

Since m∠W + m∠X + m∠Y = 180°

m∠W + 26° + 130° = 180°

m∠W = 180° - 156°

m∠W = 24°

$\frac{\text{Sin24}}{\text{XY}}=\frac{\text{Sin130}}{31}=\frac{\text{Sin26}}{\text{WX}}$

$\frac{\text{Sin24}}{\text{XY}}=\frac{\text{Sin130}}{31}$

XY = $\frac{31\times (\text{Sin24})}{\text{Sin130}}$

XY = 16.4597

     ≈ 16.4597 mm

Area of the triangle = $\frac{1}{2}(\text{XY})(\text{WY})\text{SinY}$

                                 = $\frac{1}{2}(16.4597)(31)\text{Sin26}$

                                 = 111.83 mm²

                                 ≈ 111.8 mm²

Therefore, area of the triangle WXY = 111.8 mm²