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