SOLUTION: Determine the measure of angle B of triangle ABC given the following information: C = 120° a = 6 b = 2, and my options are: 25°, 46°, 14° and 19°.

We draw the triangle:



We extend BC, and draw a line segment from A perpendicular to the 
extension of BC, intersecting it at D:



Angle ACD is 60° because it is supplementary to angle ACB which is 120°,
and 180°- 120° = 60°


 
Triangle ADC is a "30°60°90°" right triangle, and since its          _
hypotenuse AC is 2, its lower leg CD is 1, and its vertical leg AD is √3.
BD = BC + CD = 6 + 1 = 7 



Triangle ADB is a right triangle, therefore

tan(B) =  = 

Use inverse tangent function to get

Angle B = 13.89788625° closest to 14°.

Edwin