Доказать,что треугольник с вершинами А(2;1) В(3;0) С(1;5) тупоугольный,и найти косинус тупого угла.
AB^2= (3-2)^2+(0-1)^2=2; AC^2=(2-1)^2+(1-5)^2=17; BC^2= (3-1)^2+(0-5)^2=29;
cos(A)=-(BC^2-AC^2-AB^2)/(2*AB*AC)=-(29-17-2)/(2*sqrt(17*2))=-5/sqrt(34);
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AB^2= (3-2)^2+(0-1)^2=2; AC^2=(2-1)^2+(1-5)^2=17; BC^2= (3-1)^2+(0-5)^2=29;
cos(A)=-(BC^2-AC^2-AB^2)/(2*AB*AC)=-(29-17-2)/(2*sqrt(17*2))=-5/sqrt(34);