Solve the all parts of following question given below:
Question: Captain Jack Sparrow has been marooned on an island in the Atlantic by his crew, and decides to build a raft to escape. The wind seems quite steady, and first blows him due east for 15 km, and then 10 km in a direction 8 degrees north of east. Confident that he will eventually find himself in safety, he falls asleep. When he wakes up, he notices the wind is now blowing him gently 12 degrees south of east - but after traveling for 21 km, he finds himself back on the island!
Part I: How far (in km) did the wind blow him while he was sleeping?
Part II: Assuming the wind blew the same direction all night, what direction, in degrees north of west, did the wind blow Jack during the night?
Please explain each step and equations used for above question.