| A(20;40) B(80;40) C(60;20) |
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a²=(B(x)-C(x))²+(B(y)-C(y))²=(80-60)²+(40-20)²=20²+20²=400+400=800 | a=√800=28.284
b²=(C(x)-A(x))²+(A(y)-C(y))²=(60-20)²+(40-20)²=40²+20²=1600+400=2000 | b=√2000=44.721 c²=(B(x)-A(x))²+(B(y)-A(y))²=(80-20)²+(40-40)²=60²+0²=3600+0=3600 | c=√3600=60 |
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a²=b²+c²-2bc cos α | cos α=(b²+c²-a²)/2bc = (2000+3600-800)/(2×44.721×60)=4800/5366.52=0.894 | α=arccos 0.894 = 26.564°
b²=a²+c²-2ac cos β | cos β=(a²+c²-b²)/2ac = (800+3600-2000)/(2×28.284×60)=2400/3394.08=0.707 | β=arccos 0.707 = 45° c²=a²+b²-2ab cos γ | cos γ=(a²+b²-c²)/2ab = (800+2000-3600)/(2×28.284×44.721)=-800/2529.8=-0.316 | γ=arccos -0.316 = 108.435° |