Question

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Answer 1

Answer:

Area of the triangle = 469.4 ft²

Step-by-step explanation:

By applying Sine rule in the given triangle WXY,

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

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,

$\frac{\text{Sin27}}{\text{XY}}=\frac{\text{SIn40}}{38}=\frac{\text{Sin113}}{\text{WY}}$

$\frac{\text{Sin27}}{\text{XY}}=\frac{\text{SIn40}}{38}$

XY = $\frac{38\text{(Sin27)}}{\text{Sin40}}$

XY = 26.84

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

                                = $\frac{1}{2}(26.84)(38)(\text{Sin113})$

                                = 469.42

                                ≈ 469.4 ft²