现有三个村庄,村庄B在村庄A的南偏东60度方向,村庄C在村庄A的南偏东80度方向,村庄B在村庄C的南偏西45度方

2个回答

  • 郭敦顒回答:

    如图,∠BAF=60°,∠CAF=80°,∠BAC=80°-60°=20°,∠CAD=10°

    过B作EF⊥Y轴于F,过C作DE⊥X轴于D,交EF于E,则

    DE=AF=3,AD=FE.

    设AB=6,则FB=6sin60°=5.1962,AF=6 cos60°=3,

    B村坐标为B(5.1962,-3).

    按正弦定理:a/sinA=b/sinB=c/sinC,

    BC/sin20°=AC/sin105°=6/sin55°=7.3246,

    BC=7.3246 sin20°=2.5052,

    AC= 7.3246 sin105°=7.075

    AD=AC cos10°=7.075cos10°=6.9675,CD=7.075sin10°=1.2286,

    C村坐标为C(6.9675,-1.2286).

    CE=BE=BC×(1/2)√2=2.5052×(1/2)√2=1.7714,

    DE=1.2286+1.7714=3,对照相符.

    Y(北)

    X ′(西) O A(0,0) D(6.9675,0) X(东)

    10°

    60°20° 80° C(6.9675,-1.2286)

    6 55°

    105° 45°

    30° 45° E(6.9675,-3)

    F(0,-3)B(5.1962,-3)

    Y′(南)