Question 1080908
So let the equal side be N.
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*[illustration SD1.png].
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From the perimeter you know,
{{{2N+B=18}}}
{{{B=18-2N}}}
The height of the triangle would be obtained using the base and N using the Pythagorean theorem,
{{{N^2-(B/2)^2=H^2}}}
with the condition,
{{{N^2>=(B/2)^2}}}
{{{N^2>=(9-N)^2}}}
{{{N^2>81-18N+N^2}}}
{{{81-18N<0}}}
{{{-18N<-81}}}
{{{N>81/18}}}
{{{N>9/2}}}
Since N is an integer,
{{{N>=5}}}
Also, 
{{{2N+B=18}}}
{{{B>0}}} so,
{{{2N<18}}}
{{{N<9}}}
So,
{{{5<=N<=8}}}
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For the angle the information already given,
{{{sin(theta)=H/N}}}
{{{sin(theta)=sqrt(N^2-(B/2)^2)/N}}}
Make a table of values,
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*[illustration 239.JPG].