Step-by-step explanation:
Let a = 8 and b = 11. Using the law of cosines, we can write
[tex]c^2 = a^2 + b^2 - 2ab\cos{c}[/tex]
[tex]\:\:\:\:=(8)^2 + (11)^2 - 2(8)(11)\cos{37} = 44.44[/tex]
[tex]c = 6.67[/tex]
Now we're going to use the sine to find [tex]\angle{B}:[/tex]
[tex]\dfrac{\sin{B}}{b} = \dfrac{\sin{37}}{c}[/tex]
or
[tex]\sin{B} =\left(\dfrac{b}{c}\right)\sin{37} = 0.992[/tex]
or
[tex]B = \sin^{-1}(0.992) = 83.0°[/tex]
