Question 1008804
I assume that {{{a=4}}} and {{{b=13}}} are measures of the sides.
Use the law of cosines to find the unknown side, {{{c}}}.
{{{c^2=a^2+b^2-2ab*cos(C)}}}
{{{c^2=4^2+13^2-2(4)(13)*cos(45)}}}
{{{c^2=16+169-104*(sqrt(2)/2)}}}
{{{c^2=111.461}}}
{{{c=10.56}}}
Then use the law of sines,
{{{a/sin(A)=c/sin(C)}}}
{{{4/sin(A)=10.56/sin(45)}}}
{{{sin(A)=(4*sin(45))/10.56}}}
{{{sin(A)=0.2679}}}
{{{A=15.5}}}