Đáp án: $AH=57.12, HB=42.84, HC=76.16$
Giải thích các bước giải:
Ta có $BC=BD+DC=119$
Vì $AD$ là phân giác $\hat A$
$\to \dfrac{DB}{DC}=\dfrac{AB}{AC}$
$\to\dfrac{AB}{AC}=\dfrac34$
$\to \tan\widehat{ACB}=\dfrac{AB}{AC}=\dfrac34$
$\to \tan\widehat{ACH}=\dfrac34$
$\to \dfrac{AH}{HC}=\dfrac34$
$\to HC=\dfrac43AH$
Mà $AH^2=HB.HC$
$\to AH^2=HB.\dfrac43AH$
$\to AH=HB.\dfrac43$
$\to HB=\dfrac34AH$
$\to BC=HB+HC=\dfrac34AH+\dfrac43AH=\dfrac{25}{12}AH$
$\to \dfrac{25}{12}AH=119$
$\to AH=57.12$
$\to HB=42.84, HC=76.16$
