An offshore lighthouse is 2 kilometers from a Coast Guard station C and 2.5 kilometers from a hospital H near the shoreline. If the angle formed by light beams to C and H is 143o, what is the distance CH (by sea) between the Coast Guard station and the hospital? Provide a real-life scenario in which vectors must be used to answer the question. Provide the solution as well

"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?