Theo hệ thức lượng trong tam giác vuông ta có: $AH^2=HB.HC=48^2$
Có $\dfrac{HB}{HC}=\dfrac{9}{16}$
$⇒\dfrac{HB.HC}{HC^2}=\dfrac{9}{16}$
$⇒\dfrac{48^2}{HC^2}=\dfrac{9}{16}$
$⇒HC=64(cm)⇒HB=36(cm)$
$⇒BC=100$
$⇒AB^2=BH.BC=36.100⇒AB=60(cm)$
$AC^2=CH.BC=64.100⇒AC=80(cm)$