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�.

Question 398510: 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�.

Answer by Edwin McCravy(20054) (Show Source): You can put this solution on YOUR website!


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

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