Answer: The value of b is approximately 54.94 .
Explanation:
In the given figure two angles are given and according to the angle sum property the sum of interior angles of a triangle is 180 degree.
[tex]\angle A+\angle B+\angle C=180[/tex]
[tex]42+\angle B+41.5=180[/tex]
[tex]\angle B=180-83.5[/tex]
[tex]\angle B=96.5[/tex]
According to the law of sine,
[tex]\frac{a}{\sin A} =\frac{b}{\sin B} =\frac{c}{\sin C}[/tex]
From given figure, [tex]\angle A=42,a=37[/tex]
[tex]\frac{37}{\sin (42^{\circ})}= \frac{b}{\sin (96.5^{\circ})}[/tex]
[tex]\frac{37}{0,66913} =\frac{b}{0.99357}[/tex]
[tex]b=54.94018[/tex]
[tex]b\approx 54.94[/tex]
Therefore, the value of b is 54.94.
