a) Vì $\frac{AB}{AC}$ = $\frac{8}{15}$ ⇒ Đặt AB=8k, AC=15k (k > 0)
Ta có: $BC^{2}$ = $AB^{2}$ + $AC^{2}$ = $(8k)^{2}$ + $(15k)^{2}$ (Định lí Pitago)
⇔ $34^{2}$ = $64k^{2}$ + $225k^{2}$
⇔ 1156 = 289$k^{2}$
⇔ $k^{2}$ = 4 ⇔ k = 2
⇒ AB = 8.2 = 16cm
AC = 15.2 = 30cm
b) Theo HTL Δ vuông:
AH = $\frac{AB.AC}{BC}$ = $\frac{16.30}{34}$ = $\frac{240}{17}$ cm
BH = $\frac{AB^2}{BC}$ = $\frac{16^2}{34}$ = $\frac{128}{17}$ cm
CH = $\frac{AC^2}{BC}$ = $\frac{30^2}{34}$ = $\frac{450}{17}$ cm
