Luke sailed for 116 kilometres on a bearing of 231^\circ .

If w is how many kilometres west he has sailed from his starting point, find $w$ to one decimal place.
Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.
Question: Luke sailed for 116 kilometres on a bearing of 231^\circ .

If w is how many kilometres west he has sailed from his starting point, find $w$ to one decimal place.
Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.
Question: Luke sailed for 116 kilometres on a bearing of 231^\circ .

If w is how many kilometres west he has sailed from his starting point, find $w$ to one decimal place.