On my tourist map of Quebec, the distance between the dots representing Montreal and Quebec City is 10 cm. If the scale of the map is 4/9 mm = 1 km, then how far apart are Montreal and Quebec City? (Note that 10 mm = 1 cm)

"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?