Question 483793
<pre>
{{{drawing(400,250,-.5,7.5,-.5,4.5,

triangle(0,0,5.7,0,6.71666666666,3.765154564),
locate(0,0,B), locate(5.7,0,C), locate(6.7,4.1,A),
locate(2.2,0,a=5.7), locate(6.3,1.8,b=3.9),locate(2.2,2,c=7.7)
arc(5.7,0,1,-1,74.889,180)
 )}}}

Use the law of cosines

{{{cos(C)=(a^2+b^2-c^2)/(2ab)}}}

{{{cos(C)=(5.7^2+3.9^2-7.7^2)/(2(5.7)(3.9))}}}

{{{cos(C)=(32.49+15.21-59.29)/44.46}}}

{{{cos(C)=(-11.59)/44.46}}}

{{{cos(C) = -.2606837607}}}

Use the inverse cosine function on your calculator,
being sure it is in degree mode, not radian mode.

{{{C = "105.1106379°"}}}

to the nearest whole degree is 105°

Edwin</pre>