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reality227
@reality227
October 2021
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в Треугольнике даны две стороны a и b,площадь S.Найди 3 сторону,и радиусы вписанной и описанной окружностей.
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Verified answer
S=a*b*sin(fi)/2
sin(fi)=2S/(a*b)
cos(fi)=корень(1-sin^2(fi))=корень(1-(2S/(a*b))^2)
c=корень(a^2+b^2-2*a*b*cos(fi))= корень(a^2+b^2-2*a*b*корень(1-(2S/(a*b))^2) )
r=2S/(a+b+c)=2*S/(a+b+ корень(a^2+b^2-2*a*b*корень(1-(2S/(a*b))^2) ) )
R=abc/(4S)=a*b* корень(a^2+b^2-2*a*b*корень(1-(2S/(a*b))^2) )/(4*S)
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Answers & Comments
Verified answer
S=a*b*sin(fi)/2sin(fi)=2S/(a*b)
cos(fi)=корень(1-sin^2(fi))=корень(1-(2S/(a*b))^2)
c=корень(a^2+b^2-2*a*b*cos(fi))= корень(a^2+b^2-2*a*b*корень(1-(2S/(a*b))^2) )
r=2S/(a+b+c)=2*S/(a+b+ корень(a^2+b^2-2*a*b*корень(1-(2S/(a*b))^2) ) )
R=abc/(4S)=a*b* корень(a^2+b^2-2*a*b*корень(1-(2S/(a*b))^2) )/(4*S)