Question 728368
{{{sin(beta)/b=sin(gamma)/c}}}
{{{sin(gamma)=c*sin(beta)/b}}}
Plugin the values:
{{{sin(gamma)=6*sin(76)/13}}}
{{{sin(gamma)=0.4478}}}
{{{highlight(gamma = 26.6)}}} degrees.


You have two angles of the triangle and you can use sum to 180 degrees to find the measure of angle alpha.


{{{76+26.6+alpha=180}}}
{{{highlight(alpha=77.4)}}} degrees.


Use Law of Sines again to find the length of a.  
{{{sin(alpha)/a=sin(beta)/b}}}
{{{a/sin(alpha)=b/sin(beta)}}}
{{{a=b*sin(alpha)/sin(beta)}}}
{{{a=13*sin(77.4)/sin(76)}}}
a=... What do you get?  This should be very very near 13.