Answer: 5.22
Step-by-step explanation:
Given
[tex]\angle A=103^{\circ}[/tex]
Sine law is [tex]\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}\\[/tex]
Here, a=8, c=5
Putting values
[tex]\Rightarrow \dfrac{8}{\sin 103}=\dfrac{5}{\sin C}\\\\\Rightarrow \sin C=\dfrac{5}{8}\sin 103^{\circ}=0.6089\\\Rightarrow C=37.51^{\circ}[/tex]
[tex]\Rightarrow \angle B=180^{\circ} -103^{\circ}-37.51^{\circ}\\\Rightarrow \angle B=39.49^{\circ}[/tex]
If b=m, then
[tex]\Rightarrow \dfrac{8}{\sin 103^{\circ}}=\dfrac{m}{\sin 39.49^{\circ}}\\\\\Rightarrow m=\dfrac{\sin 39.49^{\circ}}{\sin 103^{\circ}}\times 8=5.22[/tex]
