Here's why:
* Precipice: A very steep cliff or rock face, often at the edge of a mountain or a body of water. It implies a dangerous drop-off.
Let's look at the other words:
* Gnarly: This word describes something twisted, knotted, or rough, often in a visually appealing way. It doesn't directly relate to an edge.
* Rivulet: A small stream or brook. While it can be found at the edge of a larger body of water, it doesn't have the same sense of danger or steepness as a precipice.
* Cascade: A waterfall or a series of waterfalls. While cascades often have an edge, the word itself doesn't specifically refer to the edge.
Therefore, "precipice" is the word that most closely associates with the concept of an edge, particularly a dangerous or dramatic one.