Answer:
6.8 inches
Step-by-step explanation:
Given data :
m∠ A = 53° , m∠ C = 84° , side a = 8 inches
therefor m ∠ B = ( 180 - (84 + 53 )) = 43°
Find the length of side b
we will apply sine rule here
[tex]\frac{a}{sinA} = \frac{b}{sinB} = \frac{c}{sinC}[/tex]
= [tex]\frac{8}{sin53}[/tex] = [tex]\frac{b}{sin43}[/tex]
∴ b = ( sin43° * 8 ) / sin53°
= ( 0.6819 * 8 ) / 0.7986
= 5.4552 / 0.7986 = 6.83 ≈ 6.8 inches
