Ta có :
\(\cot\left(B\right)=\dfrac{BH}{AH}\Leftrightarrow\dfrac{1}{\tan\left(42\right)}=\dfrac{BH}{AH}\)
\(\cot\left(C\right)=\dfrac{HC}{AH}\Leftrightarrow\dfrac{1}{\tan\left(35\right)}=\dfrac{HC}{AH}\)
Cộng vế theo vế được :
\(\dfrac{BH}{AH}+\dfrac{HC}{AH}=\dfrac{1}{\tan\left(42\right)}+\dfrac{1}{\tan\left(35\right)}\)
\(\Leftrightarrow\dfrac{BH+HC}{AH}=2,538760522\)
\(\Leftrightarrow\dfrac{BC}{AH}=2,538760522\)
\(\Leftrightarrow\dfrac{7}{AH}=2,538760522\)
\(\Leftrightarrow AH=\dfrac{7}{2,538760522}=2,757251005cm\)
Vậy \(AH=2,757251005cm\)
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