Three 24-hour clocks show the time to be 12 noon. one of the clocks is always correct, one loses a time every 24 hours, and one gains for a minute every 24 hours. how many days will pass before all three clocks show the correct time again?

"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?