Question 368944
Use the law of sines,
{{{a/sin(A)=b/sin(B)=c/sin(C)}}}
{{{6/sin(10)=13/sin(B)}}}
{{{sin(B)=(13/6)sin(10)}}}
{{{sin(B)=0.3762}}}
{{{B=22.1}}}degrees
Since
{{{A+B+C=180}}}
{{{10+22.1+C=180}}}
{{{C=147.9}}}
{{{c/sin(147.9)=6/sin(10)}}}
{{{c=18.36}}}
Use Heron's formula to find the area,
{{{A=sqrt(s(s-a)(s-b)(s-c))}}}
.
.
.
{{{s=(1/2)(a+b+c)}}}
{{{s=(1/2)(6+10+18.36)}}}
{{{s=18.68}}}
.
.
{{{A=sqrt(18.68(18.68-6)(18.68-10)(18.68-18.36))}}}
{{{highlight(A=20.75)}}}