Answer:
D
Step-by-step explanation:
Using the Sine rule to find a and b
We require to find ∠ C
∠ C = 180° - (115 + 43)° = 180° - 158° = 22°
Then
[tex]\frac{a}{sinA}[/tex] = [tex]\frac{c}{sinC}[/tex] , substitute values
[tex]\frac{a}{sin43}[/tex] = [tex]\frac{6}{sin22}[/tex] ( cross- multiply )
a × sin22° = 6 × sin43° ( divide both sides by sin22° )
a = [tex]\frac{6sin43}{sin22}[/tex] ≈ 10.92 ( to 2 dec. places )
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[tex]\frac{b}{sinB}[/tex] = [tex]\frac{c}{sinC}[/tex] , that is
[tex]\frac{b}{sin115}[/tex] = [tex]\frac{6}{sin22}[/tex] ( cross- multiply )
b × sin22° = 6 × sin115° ( divide both sides by sin22° )
b = [tex]\frac{6sin115}{sin22}[/tex] ≈ 14.52 ( to 2 dec. places )
