Question 766551
A drawing would be according to angle at C is 92 degrees.  Side length opposite A is a; side length opposite B is b; side length opposite C is c.  


Given perimeter means {{{a+b+c=400}}}.
Law of Sines gives:
{{{sin(30)/a=sin(58)/b}}}
{{{sin(58)/b=sin(92)/c}}}
{{{sin(30)/a=sin(92)/c}}}
A couple more equations that come from them are:
{{{b=a*sin(58)/sin(30)}}} and {{{c=b*sin(92)/sin(58)}}}


Use those last two to substitute into the perimeter.
Also make use of the b= equation again since b still shows in this substitution.
{{{a+a*sin(58)/sin(30)+(a*sin(58)/sin(30))(sin(92)/sin(58))=400}}}
.some couple steps..
.calculator or table of trigonometric function values...
{{{a*(4.6949)=400}}}
{{{highlight(a=85.1992)}}}


From that, other simpler law of sine relationships give {{{highlight(b=144.506)}}} and {{{highlight(c=170.2948)}}}