Question 879347
<pre>
This is a case of SAS, so we use the law of cosines.

{{{drawing(300,255,-.5,5.5,-.5,4.6,triangle(0,0,5,0,4*cos(50*pi/180),4*sin(50*pi/180)),locate(.3,.3,"50°"), locate(2.5,0,a=5),locate(.6,1.7,b=4),
locate(4,1.7,c), locate(0,0,C), locate(5,0,B), locate(2.6,3.2,A)


 )}}}

{{{c^2}}}{{{""=""}}}{{{a^2+b^2-2*a*b*cos(C)}}}

{{{c^2}}}{{{""=""}}}{{{4^2+5^2-2*4*5*cos("50°")}}}

{{{c^2}}}{{{""=""}}}{{{16+25-40*cos("50°")}}}

{{{c^2}}}{{{""=""}}}{{{41-40*(.6427876097)}}}

{{{c^2}}}{{{""=""}}}{{{15.28849561}}}

{{{c}}}{{{""=""}}}{{{sqrt(15.28849561)}}}

{{{c}}}{{{""=""}}}{{{3.91005059}}}

You can either finish by using the law of sine or 
you can use the law of cosines again.

{{{cos(A)}}}{{{""=""}}}{{{(b^2+c^2-a^2)/2bc}}}


You already have cē = 15.28849561

{{{cos(A)}}}{{{""=""}}}{{{(4^2+15.28849561-5^2)/(2*4*15.28849561)}}}

{{{cos(A)}}}{{{""=""}}}{{{(4^2+15.28849561-5^2)/(2*4*3.91005059)}}}

A = 78.4024367

Then to find C add those angles and subtract from 180°

B = 51.5975633

Edwin</pre>