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Please answer this question now-example-1

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Answer:

Area of the triangle = 469.4 ft²

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 =
(1)/(2)(\text{XY})(\text{XW})(\text{SinX})

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

= 469.42

469.4 ft²

User Abourget
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