Explanation
Let's first make a sketch of the triangle:
We can find the measure of c with the law of cosines:
[tex]c=\sqrt{a^2+b^2-2ab\cdot cos(C)}[/tex][tex]c=\sqrt{9+16-24\cdot\frac{1}{2}}[/tex][tex]c=\sqrt{13}[/tex]
For B and A we can use the sine law:
[tex]\frac{sin(B)}{3}=\frac{sin(60)}{\sqrt{13}}[/tex][tex]B=73.898°[/tex]
And
[tex]\frac{sin(A)}{4}=\frac{sin(60)}{\sqrt{13}}[/tex][tex]A=46.102°[/tex]
Answer
[tex]c=\sqrt{13}[/tex][tex]B=73.898°[/tex][tex]A=46.102°[/tex]
