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 $19km,$ and then $11\mathrm{.}5km$ in a direction $6\mathrm{.}5$ degrees north of east.

Part $($c$)$ Confident that he will eventually find himself in Spain, Jack falls asleep. When he wakes up$,$ he notices the wind is blowing him gently at $14$ degrees south of east $-$ but after traveling for $23km,$ he finds himself back on the island where he started! How far, in kilometers, did the wind blow him while he w sleepinG$|$