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)