Question

Answer 1

a) \(AB^2=BC^2+AC^2-2BC.AC.cosC\)

Nên câu a Sai

b) \(cosA=\dfrac{AB^2+AC^2-BC^2}{2.AB.AC}=\dfrac{25+64-49}{2.5.8}=\dfrac{1}{2}\)

\(\Rightarrow A=60^o\)

Nên câu b Sai

c) \(m_a^2=\dfrac{2\left(AB^2+AC^2\right)-BC^2}{4}=\dfrac{2\left(25+64\right)-49}{4}=\dfrac{129}{4}\)

\(\Rightarrow m_a=\dfrac{\sqrt{129}}{2}\)

Nên câu c Sai

d) \(cosB=\dfrac{AB^2+BC^2-AC^2}{2.AB.BC}=\dfrac{25+49-64}{2.5.7}=\dfrac{1}{7}\)

\(MC=2MB\Rightarrow BM=\dfrac{BC}{3}=\dfrac{7}{3}\)

\(AM^2=BM^2+AB^2-2BM.AB.cosB\)

\(\Rightarrow AM^2=\dfrac{49}{9}+25-2.\dfrac{7}{3}.5.\dfrac{1}{7}=\dfrac{304}{9}\)

\(\Rightarrow AM=\dfrac{2\sqrt{76}}{3}\)

Nên câu d Sai