Question

Cho tam giác ABC vuông tại A tính BH,CH, AC ,AH biết:

 AB =12 cm BC= 13cm

Answer 1

Ta có: \(AC=\sqrt{BC^2-AC^2}=\sqrt{13^2-12^2}=5\left(cm\right)\)

Ta có: \(AH.BC=AB.AC\Rightarrow AH=\dfrac{AB.AC}{BC}=\dfrac{12.5}{13}=\dfrac{60}{13}\left(cm\right)\)

Ta có: \(\left\{{}\begin{matrix}AB^2=BH.BC\\AC^2=CH.BC\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}BH=\dfrac{AB^2}{BC}=\dfrac{12^2}{13}=\dfrac{144}{13}\left(cm\right)\\CH=\dfrac{AC^2}{BC}=\dfrac{5^2}{13}=\dfrac{25}{13}\left(cm\right)\end{matrix}\right.\)