Answer:
b = 8.89, c = 11.96 and m∠B = 48°
Step-by-step explanation:
From the given triangle ABC,
We will apply sine ratio for angle A,
sin(A) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
sin(42)° = [tex]\frac{BC}{AB}[/tex]
sin(42)° = [tex]\frac{8}{AB}[/tex]
AB = [tex]\frac{8}{\text{sin}(42)}[/tex]
AB = 11.96
c = 11.96
By triangle sum theorem,
m∠A + m∠B + m∠C = 180°
42° + m∠B + 90° = 180°
m∠B = 180 - 132
m∠B = 48°
By cosine ratio of angle A,
cos(A) = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]
cos(42)° = [tex]\frac{AC}{AB}[/tex]
AC = AB.cos(42)°
AC = (11.96)cos(42)°
AC = 8.89
b = 8.89