What is the vertex angle of an isosceles triangle with a base one third the length of the sides?

Question

The sides are three times the side of the base

Answer 1

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.