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kristinacheren
@kristinacheren
November 2021
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Найдите косинус угла А треугольника АВС, если А(3; 9), В(0; 6), С(4; 2).
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Незнaйкa
AB^2=(3-0)^2+(9-6)^2=9+9=18
AB=V18=3V2
BC^2=(4-0)^2+(2-6)^2=16+16=32
BC=V32=4V2
AC^2=(4-3)^2+(2-9)^2=1+49=50
AC=V50=5V2
По т. Косинусов. BC^2=AC^2+AB^2-2•AC•AB•cosA
СоsA=(AC^2+AB^2-BC^2)/2•AC•AB
cosA=(50+18-32):2•5V2•3V2=36/60=3/5
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Answers & Comments
AB=V18=3V2
BC^2=(4-0)^2+(2-6)^2=16+16=32
BC=V32=4V2
AC^2=(4-3)^2+(2-9)^2=1+49=50
AC=V50=5V2
По т. Косинусов. BC^2=AC^2+AB^2-2•AC•AB•cosA
СоsA=(AC^2+AB^2-BC^2)/2•AC•AB
cosA=(50+18-32):2•5V2•3V2=36/60=3/5