In this article, the classic problem of finding three ways to determine the probability that the pieces of a stick randomly broken in two places will form a triangle is analyzed anew. To be useful in the classroom, an application must be incorporated into an often-crowded curriculum. What is nice about this triangle problem is that it fits in naturally at many different points. The first method discussed in this article could be used to introduce the topic of geometric probabilities or as an enrichment exercise after a lesson in graphing inequalities. The second method involves a rather straightforward use of a three-dimensional graph and could be used to help students get used to working in a three-dimensional setting. The third method could be presented when reviewing locus or equilateral triangle geometry. (Contains 8 figures.)