Question 892409
You can use the law of sines.
Let the three angles be {{{A}}},{{{B}}} and {{{C}}}.
Let the three corresponding sides be {{{a}}},{{{b}}}, and {{{c}}}.
You know,
{{{a+b+c=240}}}
From the law of sines you know,
{{{sin(A)/a=sin(B)/b=sin(C)/c}}}
So then from this,
{{{b*sin(A)=a*sin(B)}}}
{{{b=a(sin(B)/sin(A))}}}
and
{{{c*sin(A)=a*sin(C)}}}
{{{c=a(sin(C)/sin(A))}}}
Substituting,
{{{a+a(sin(B)/sin(A))+a(sin(C)/sin(A))=240}}}
{{{a(1+sin(B)/sin(A)+sin(C)/sin(A))=240}}}
Then you find {{{a}}} and work backwards to find {{{b}}} and {{{c}}}.