The mean waiting time at the drive-through of a fast-food restaurant from the time an order is placed to the time the order is received is seconds. A manager devises a new drive-through system that believes will decrease wait time. As a test, initiates the new system at restaurant and measures the wait time for randomly selected orders. The wait times are provided in the table to the right. Complete parts (a) and (b) below.

"curse these trig-loving pirates! " devora mutters as she looks at the map. then, after thinking for a moment, she walks back to the entrance of the secret cave, measuring 48 meters along the way. after performing a calculation, devora walks back to the empty treasure, faces the entrance, and turns a certain number of degrees to her left before walking 89 meters to the treasure. supposing that the angle at the cave entrance is acute and that devora's calculations were correct, how many degrees did she turn?