$\text{Theo định lý Py - ta - go, ta có:}$
$AH^{2}$ + $HC^{2}$ = $AC^{2}$
$\text{Hay: }$$12^{2}$ + $16^{2}$ = $\text{400}$
$\text{→ AC = }$$\sqrt[]{400}$ = $\text{20}$
$AH^{2}$ + $BH^{2}$ = $AB^{2}$
$\text{Hay: }$$12^{2}$ + $9^{2}$ = $\text{225}$
$\text{→ AB = }$$\sqrt[]{225}$ = $\text{15}$
$\text{Lại có: }$
$BC^{2}$ = $25^{2}$ = $\text{625}$
$AB^{2}$ $\text{+}$ $AC^{2}$ = $20^{2}$ + $15^{2}$ = $\text{625}$
$\text{→}$ $AB^{2}$ $\text{+}$ $AC^{2}$ = $BC^{2}$
$\text{→ ΔABC là tam giác vuông}$
$\text{→}$ `hat{BAC}` $\text{=}$ $90^{o}$
