Cho tam giac ABC có cosA=5/9 , D thuộc cạnh BC sao cho (ABC) ̂=(DAC) ̂, DA=6, BD=16/3. Tính chu vi tam giác ABC.

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Cho tam giac ABC có  , D thuộc cạnh BC sao cho , DA=6, . Tính chu vi tam giác ABC.

 

Giải:

Xét 2 tam giác ABC và ADC ta có:

ü 

ü   chung

ð  ABCDAC

ð 

Ta cũng có:

Mà cos=-cos()

Nên: cos=-cos

=>

=>AB2=AD2+BD2-2AD.BD.cos

 

=>

Thay vào biểu thức đồng dạng ở trên ta có:

Ta có hệ:

 

=>AC2=DC.BC==40,96

=>AC=6,4

Vậy chu vi tam giác ABC là:

AB+AC+BC=9+6,4+9,6=25

Comments

  1. AnonymousAugust 24, 2022 at 4:22 AM

    vẫn đang thắc mắc là 81 vs 36 đâu ra=)))

    ReplyDelete

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