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
2个回答

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°