Answer:
m∠B = 100°
a = 4.6
b = 7.36
Step-by-step explanation:
By applying sine rule in the given triangle,
[tex]\frac{\text{sin(A)}}{a}= \frac{\text{sin(B)}}{b}= \frac{\text{sin(C)}}{c}[/tex]
Now substitute the values in the expression,
[tex]\frac{\text{sin(38)}}{a}= \frac{\text{sin(B)}}{b}= \frac{\text{sin(42)}}{5}[/tex]
[tex]\frac{\text{sin(38)}}{a}= \frac{\text{sin(42)}}{5}[/tex]
[tex]a=\frac{5\text{sin(38)}}{\text{sin(42)}}[/tex]
a = 4.6
By applying triangle sum theorem in ΔABC,
m∠A + m∠B + m∠C = 180°
38° + m∠B + 42° = 180°
m∠B = 180° - 80°
m∠B = 100°
[tex]\frac{\text{sin(100)}}{b}= \frac{\text{sin(42)}}{5}[/tex]
[tex]b=\frac{5\text{sin(100)}}{\text{sin(42)}}[/tex]
b = 7.36
