Question 1181859
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The given information makes it possible to use the law of cosines to find the length of AC.  But I think I would go a different route.<br>
In triangle ACD, draw altitude DE to side AC.  Since the triangle is isosceles, that makes DEC and DEA congruent right triangles.  Then use<br>
{{{sin(35)=CE/10}}}<br>
to find CE and double that to find AC.<br>
Then, knowing AC, use<br>
{{{tan(32)=AB/AC}}}<br>
to find AB.<br>