Question 43275
At first use sine rule.
{{{b/sin(B) = c/sin(C)}}}
or {{{b/sin(20^o) = 16/sin(115^o)}}}
or {{{b = 16*sin(20^o)/sin(115^o)}}}
or {{{b = 16*sin(20^o)/sin(180^o - 65^o)}}}
or {{{b = 16*sin(20^o)/sin(65^o)}}}
or {{{b = 16*0.342/0.906}}}
or {{{b = 6.038}}}


Now, in triangle ABC sum of the internal angles = {{{180^o}}}.
So, {{{A + B + C = 180^o}}}
or {{{A + 20^o + 115^o = 180^o}}}
or {{{A = 180^o - 20^o - 115^o}}}
or {{{A = 45^o}}}


Now, area of triangle ABC is {{{(1/2)b*c*sin(A)}}} = {{{(1/2)6.038*16*sin(45^o)}}} = 34.156 sq units.