Đáp án:
\(AH = 6,72;\,\,BH = 1,96.\,\,\,CH = 4,76.\)
Giải thích các bước giải:
\(\begin{array}{l}
Gia\,\,su\,\,\Delta ABC\,\,vuong\,\,tai\,\,A,\,\,\,duong\,\,cao\,\,AH.\\
AB = 7,\,\,\,AC = 24.\\
Ap\,\,dung\,\,dinh\,\,ly\,\,Pitago\,\,ta\,\,co:\\
BC = \sqrt {A{B^2} + A{C^2}} = \sqrt {{7^2} + {{24}^2}} = 25.\\
Ap\,\,dung\,\,he\,\,thuc\,\,\,luong\,\,trong\,\,tam\,\,giac\,\,vuong\,\,ta\,\,co:\\
AB.AC = AH.BC \Rightarrow AH = \frac{{AB.AC}}{{BC}} = \frac{{7.24}}{{25}} = 6,72.\\
A{B^2} = BH.BC \Rightarrow BH = \frac{{A{B^2}}}{{BC}} = \frac{{{7^2}}}{{25}} = 1,96.\\
CH = BC - BH = \frac{{168}}{{25}} - \frac{{49}}{{25}} = \frac{{119}}{{25}} = 4,76.
\end{array}\)
