Question

Please answer this question now

Answer 1

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