The length of the baltimore beltway is 51.6 miles. assuming the beltway was a perfect circle with a radius of 8.21 miles, and the angle between exits 7 and exit 36 is 2.54 radians, find the distance traveled.

"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?