Verified answer

Ответ:

1) AB=7ед;

∠А=38°

∠В=22°

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2) ∠В=96°; ∠С=34°; ∠А=50°

Объяснение:

1) теорема косинусов:

АВ=√(АС²+ВС²-2*АС*ВС*cos∠C)=

=√(3²+5²-2*3*5*cos120°)=√(9+25-2*15*(-½))=

=√(34+15)=√49=7 ед

cos∠A=(AC²+AB²-BC²)/(2*AC*AB)=

=(3²+7²-5²)/(2*3*7)=(9+49-25)/42=

=33/42=0,7857

∠А=arccos0,7857≈38°

∠B=180°-∠A-∠C=180°-120°-38°=22°

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2) теорема косинусов

cos∠B=(AB²+BC²-AC²)/(2*AB*BC)=

=(5²+7²-9²)/(2*5*7)=(25+49-81)/70=

=-7/70=-0,1

∠B=arccos(-0,1)=96°

cos∠C=(BC²+AC²-AB²)/(2*BC*AC)=

=(7²+9²-5²)/(2*7*9)=(49+81-25)/126=

=105/126=0,8333

∠C=arccos0,8333=34°

∠A=180°-∠B-∠C=180°-34°-96°=50°

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