数学,船A yacht sails 17 km on a bearing 104° followed by 14 km

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数学,船
A yacht sails 17 km on a bearing 104° followed by 14 km on a bearing 324°.
Calculate the distance (in km to the nearest 0.1 km) and bearing (to the nearest degree) of the yacht's final position from its initial position.
2.1 distance
2.2 bearing (°) ≈

第一问：设出发点为O,终点为B,中间点为A
那么依据题意有角OAB为40°,OA=17km,OB=14km,根据余弦定理,cosA=cos40°=（OA²+AB²-OA*AB）/2*OA*AB可以求得AB=根号下（485-476*cos40°）≈11.0km
第二问：在一问的基础上,同样根据余弦定理,可以知道cosAOB=（17*17+11*11-14*14）/2*17*11≈0.5722,查下0.5722对应的余弦值表,可以算的角AOB的度数,那么度数就是104°-角AOB

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