$a)^{}$ Theo Pi-ta-go, ta có:
$AC=\sqrt[]{AH^2+HC^2}=\sqrt[]{6^2+8^2}=\sqrt[]{100}=10^{}$ (cm)
$AB=\sqrt[]{AH^2+HB^2}=\sqrt[]{6^2+4,5^2}=\sqrt[]{56,25}=7,5^{}$ (cm)
$b)^{}$ $AB^{2}$$=100^{}$
$AC^{2}$$=56,25^{}$
$BC^{2}$$=(4,5+8)²=12,5²=156,25^{}$
$⇒^{}$ $BC^{2}$=$AB^{2}$$+AC^{2}$ $⇒ ΔABC^{}$ vuông tại $A^{}$.