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yuliya91
@yuliya91
July 2022
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В прямоугольном треугольнике ABC A = 90 градусов, AB = 65 см, высота AD = 56 см. Найдите AC и cos C.
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elenamasaeva19
BD²= AB²-AD²=65²-56²=33² ⇒ BD=33
AD=√BD*DC ⇒ DC=AD²/BD
AB=√BC*BD ⇒ BC=AB²/BD
AC=√BC*DC= √(AB²/BD)*(
AD²/BD)= (AB*AD)/BD
AC=(56*65)/33=3640/33
cosC=DC/AC=(AD
²/BD)/AC=(56²*33)/(33*56*65)=56/65
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Answers & Comments
AD=√BD*DC ⇒ DC=AD²/BD
AB=√BC*BD ⇒ BC=AB²/BD
AC=√BC*DC= √(AB²/BD)*(AD²/BD)= (AB*AD)/BD
AC=(56*65)/33=3640/33
cosC=DC/AC=(AD²/BD)/AC=(56²*33)/(33*56*65)=56/65