In the triangle \(ABC\), the angle \(A\) is equal to \(40^{\circ}\). The triangle is randomly thrown onto a table. Find the probability that the vertex \(A\) lies east of the other two vertices.
In a square with side length 1 there is a broken line, which does not self-intersect, whose length is no less than 200. Prove that there is a straight line parallel to one of the sides of the square that intersects the broken line at a point no less than 101 units along the line.