Vectors and Cliff Hanging

Why is this 200 pound climber in danger of falling even though the rope he is tied to can hold 7000 pounds?

The climber is performing what is called a Tyrolean Traverse on The Lost Arrow Spire in Yosemite Valley, California. The following picture shows a different climber traversing the same spire from another perspective.

Why isn't this climber in danger of falling?

This is the theme question that students ponder as we learn more about the mathematics of vectors. This is also the question for the Savvy Minds math puzzler contest. The solution will be posted after the last day to submit an entry, June 15th, 2008.