Question

Mn giúp em với ạ em đang cần gấp

Answer 1

Bào 7:

Áp dụng hệ thức lượng trong tam giác vuông có:

\(cos\widehat{BAH}=\dfrac{AH}{AB}=\dfrac{3}{7}\)\(\Rightarrow AH=\dfrac{3AB}{7}\)

\(AB^2+AC^2=BC^2=196\) \(\Leftrightarrow AB^2=196-AC^2\)

\(\dfrac{1}{AB^2}+\dfrac{1}{AC^2}=\dfrac{1}{AH^2}\)

\(\Leftrightarrow\dfrac{1}{196-AC^2}+\dfrac{1}{AC^2}=\dfrac{1}{\dfrac{9}{49}AB^2}\)

\(\Leftrightarrow\dfrac{1}{196-AC^2}+\dfrac{1}{AC^2}=\dfrac{49}{9\left(196-AC^2\right)}\)

\(\Leftrightarrow\dfrac{9AC^2}{9AC^2\left(196-AC^2\right)}+\dfrac{9\left(196-AC^2\right)}{9AC^2\left(196-AC^2\right)}=\dfrac{49AC^2}{9AC^2\left(196-AC^2\right)}\)

\(\Rightarrow9AC^2+9\left(196-AC^2\right)=49AC^2\)

\(\Leftrightarrow AC^2=36\) =>AC=6 

Vậy AC=6 cm