Question 15
Usain is walking for exercise by zigzagging across a $100$-meter by $30$-meter rectangular field, beginning at point $A$ and ending on the segment $\overline{BC}.$ He wants to increase the distance walked by zigzagging as shown in the figure below ($APQRS$). What angle $\theta=\angle PAB$ $=\angle QPC$ $=\angle RQB=\cdots$ will produce a length that is $120$ meters? (Do not assume the zigzag path has exactly four segments as shown; there could be more or fewer.)
