a) \(BC=BH+HC=2+6=8\)
Áp dụng hệ thức lượng ta có:
\(AH^2=BH.HC\)
\(\Rightarrow\)\(AH^2=2.6=12\)
\(\Rightarrow\)\(AH=\sqrt{12}=2\sqrt{3}\)
\(AB^2=BH.BC\)
\(\Rightarrow\)\(AB^2=2.8=16\)
\(\Rightarrow\)\(AB=4\)
\(AC^2=HC.BC\)
\(\Rightarrow\)\(AC^2=6.8=48\)
\(\Rightarrow\)\(AC=4\sqrt{3}\)
b) \(sinB=\frac{AH}{AB}=\frac{2\sqrt{3}}{4}=\frac{\sqrt{3}}{2}\)
\(cosB=\frac{BH}{AB}=\frac{2}{4}=\frac{1}{2}\)
\(tanB=\frac{AH}{BH}=\frac{2\sqrt{3}}{2}=\sqrt{3}\)
\(cotB=\frac{BH}{AH}=\frac{2}{2\sqrt{3}}=\frac{1}{\sqrt{3}}\)
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