Question

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Answer 1

927.0 cm²

Explanation:

Step 1: find Z

m < Z = 180 - (28 + 118) (sum of ∆)

= 180 - 146

Z = 34°

Step 2: Find side XY using the law of sines

`(XY)/(sin(34)) = (42)/(sin(28))`

Cross multiply

`XY*sin(28) = 42*sin(34)`

`XY*0.469 = 42*0.559`

Divide both sides by 0.469

`(XY*0.469)/(0.469) = (42*0.559)/(0.469)`

`XY = 50.06`

XY ≈ 50 cm

Step 3: find the area.

Area of ∆ = ½*XY*YZ*sin(Y)

XY ≈ 50 cm

= ½*50*42*sin(118)

= 25*42*0.8829

Area = 927.045

Area ≈ 927.0 cm² (nearest tenth)