Answer:
b = 8
c = 16
Step-by-step explanation:
From the given right triangle,
a = [tex]8\sqrt{3}[/tex], m(∠B) = 30°
By applying sine rule in the given triangle,
cos(B) = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]
cos(B) = [tex]\frac{BC}{AB}[/tex]
cos(30°) = [tex]\frac{8\sqrt{3}}{c}[/tex]
[tex]\frac{\sqrt{3} }{2}= \frac{8\sqrt{3} }{c}[/tex]
c = 16
Further we apply tangent rule,
tan(B) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
tan(30°) = [tex]\frac{b}{a}[/tex]
[tex]\frac{1}{\sqrt{3}}=\frac{b}{8\sqrt{3} }[/tex]
b = 8
