trig
posted by Bobby .
What is the angle B?
Given that
A=46 degree
b=4
c=8

Is this a triangle?
Law of Cosines:
a^2=b^2+c^22bcCosA
solve for a.
Then, law of sines:
sin46/a=sinB/b
solve for sinB, then B 
LAW OF COSINES: CosA=(b^2+c^2a^2)/2bc
Cos46=(16+64a^2)/2*4*8.
Cos46=(80a^2)/64, 80a^2=64Cos46,
a^2=8064Cos46=35.54, a=5.96=6.0
LAW of SINES: SinB/b=SinA/a
SinB/4=Sin46/6,Multiply both sides by 4: SinB=4*Sin46/6=0.4791, B=28.66=28.7 
and easy way to check this is to grab your protractor and sketch it to see if it works.