Yes, if they droped height h to the side of isoscales triangle, then from similar triangles they would have h/A=c/C and h/b=2a/c and would get the result withou

Yes, if they droped height h to the side of isoscales triangle, then from similar triangles they would have h/A=c/C and h/b=2a/c and would get the result without mention of sine rule or areas.