The surfer/spotter problem of Geometry is answered on page 290 of the Enhanced Teachers Guide for Geometry by Jacobs (ISBN: 0716756072). Since we no longer use this book, here are the two pages that solve the spotter problem.
Geometry: Surfer and the Spotter (PDF)
FYI – We now use a smaller version called “Solutions Manual Answers to Exercises for Geometry” which leaves out some of the old classroom teacher materials but is cheaper and smaller.