Let the length of the base be 2 then the equal sides will be length 6.
Drop a perpendicular bisector from the vertex angle to bisect the base.
The length of the base of the two congruent right triangles so formed is 1 and the hypotenuse is 6, so the sine of the vertex angle of each right triangle is 1/6, making the angle 9.594º. Therefore the vertex angle of the isosceles triangle is twice this=19.19º approx.