Đáp án:
$\begin{array}{l}
a)A{B^2} + A{C^2} = 4,{5^2} + {6^2} = 56,25 = 7,{5^2} = B{C^2}\\
\Rightarrow \Delta ABC\,\,vuông\,tại\,A\\
Theo\,hệ\,thức\,lượng\,trong\,tam\,giác\,ta\,có:\\
AB.AC = AH.BC\\
\Rightarrow AH = \frac{{AB.AC}}{{BC}} = \frac{{6.4,5}}{{7,5}} = 3,6\left( {cm} \right)\\
b) + )A{B^2} = BH.BC\\
\Rightarrow BH = \frac{{A{B^2}}}{{BC}} = \frac{{{6^2}}}{{7,5}} = 4,8\left( {cm} \right)\\
+ )BH + HC = BC\\
\Rightarrow HC = BC - BH = 7,5 - 4,8 = 2,7\left( {cm} \right)
\end{array}$
