Iso triangle rotation problem

There is another problem I am trying to solve maybe related to my other post I just made.

I have an Isosceles triangle with all three sides and all three angles known. One of the co equal edges of the triangle is resting on a surface. The angle that the face of the triangle makes to the table is known and is less than 90 degrees in relation to a line normal to the face of the triangle - normal line (ray) pointing away from the table or surface.

While keeping the vertex of the angle between the two equal sides of the triangle resting on the surface and acting as a pivot, and using the normal line as an axis of rotation for the triangle, how would I determine the angle of rotation for the normal line that would be required to cause the the co equal edge of the triangle to lift off of the surface, and cause both co equal lines or edges of the triangle to make equal angles to the surface (table)?