Theo định lý Pytago ta được:
$BC = \sqrt {A{B^2} + A{C^2}} = \sqrt {{7^2} + {{24}^2}} = 25(cm)$
$\begin{array}{l} A{B^2} = BH.BC\\ \Rightarrow BH = \dfrac{{A{B^2}}}{{BC}} = \dfrac{{{7^2}}}{{25}} = 1,96\left( {cm} \right)\\ CH = BC - BH = 23,04\left( {cm} \right)\\ A{H^2} = BH.CH = 45,1584\left( {cm} \right)\\ \Rightarrow AH = 6,72\left( {cm} \right) \end{array}$