Answer:
∠ B ≈ 22.0°
Step-by-step explanation:
Using the Sine Rule in Δ ABC
• [tex]\frac{a}{sinA}[/tex] = [tex]\frac{b}{sinB}[/tex] = [tex]\frac{c}{sinC}[/tex]
a, b , c are the sides opposite ∠ A, ∠ B , ∠ C , respectively.
here b = AC , c = AB , then
[tex]\frac{AC}{sinB}[/tex] = [tex]\frac{AB}{sinC}[/tex] ( substitute values )
[tex]\frac{12}{sinB}[/tex] = [tex]\frac{32}{sin93}[/tex] ( cross multiply )
32 × sin B = 12 × sin93° ( divide both sides by 32 )
sin B = [tex]\frac{12sin93}{32}[/tex] , then
∠ B = [tex]sin^{-1}[/tex] ( [tex]\frac{12sin93}{32}[/tex] ) ≈ 22.0° ( to the nearest tenth )
