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Answer:
927.0 cm²
Step-by-step 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
[tex] \frac{XY}{sin(34)} = \frac{42}{sin(28)} [/tex]
Cross multiply
[tex] XY*sin(28) = 42*sin(34) [/tex]
[tex]XY*0.469 = 42*0.559[/tex]
Divide both sides by 0.469
[tex]\frac{XY*0.469}{0.469} = \frac{42*0.559}{0.469}[/tex]
[tex]XY = 50.06[/tex]
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)