远航号货轮从A港出发,向东北方向(北偏东45°)行驶50千米,再沿北偏西30度方向行驶35千米,后沿难偏西47度行驶35

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  • 如图,∠BCD=47°+30°=77°

    BC=CD=35

    ∴∠CBD=(180°-77°)/2=51.5°

    ∠ABC=135°-30°=105°

    ∠ABD=∠ABC-∠CBD=53.5°

    △BCD中,由余弦定理:

    BD²=BC²+CD²-2BC*CDcos∠BCD

    =35²+35²-2×35×35×cos77°

    ≈1899

    △ABD中,由余弦定理:

    AD²=BD²+AB²-2BD*ABcos∠ABD

    =1899+50²-2√1899 *50cos53.5°

    =1807

    由正弦定理:AD/sin∠ABD = BD/sin∠BAD

    sin∠BAD= BDsin∠ABD / AD

    =√1899 sin53.5° / √1807

    =0.824

    ∠BAD=55.5°

    ∴∠DAE=55.5°-45°=10.5°

    即目的地在A港的北偏西10.5°