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{B C}. He wants to increase the distance walked by zigzagging as shown in the figure below (A P Q R S). What angle \theta=\angle P A B=\angle Q P C=\angle R Q B=\cdots will produce a length that is 120 meters? (The figure is not drawn to scale. Do not assume that the zigzag path has exactly four segments as shown; it could be more or fewer.)

**Answer Choices**

A. \arccos \dfrac{5}{6}

B. \arccos \dfrac{4}{5}

C. \arccos \dfrac{3}{10}

D. \arcsin \dfrac{4}{5}

E. \arcsin \dfrac{5}{6}