The law of sines is expressed as
a/SinA = b/SinB = c/SinC
Where
a, band c are sides of the triangles
A, B and C are the angles opposite the sides respectively
From the diagram,
A = 105
a = 37
c = 18
C = ?
Thus,
37/Sin105 = 18/SinC
By cross multiplying, it becomes
37SinC = 18Sin105
SinC = 18Sin105/37
SinC = 0.46991
C = arcSin0.46691
m∠C = 28
The sum of the angles in a triangle is 180 degrees. This means that
A + B + C = 180
105 + B + 28 = 180
133 + B = 180
B = 180 - 133 = 47
m∠B = 47
By applyingthe sine rule,
b/Sin47 = 37/Sin105
By cross multiplying, it becomes
bSin105 = 37Sin47
b = 37Sin47/Sin105
b = 28
The correct option is
C. m∠B=47, m∠C=28, b=28