chứng minh cho mình câu c nha, câu a,b không cần chứng minh

Bài 1. a) Ta có $\cos\widehat{BAC}=\frac{AB}{AC}=\frac{2}{4}=\frac{1}{2}$ $\Rightarrow \widehat{BAC}=60^\circ$ $\Rightarrow \widehat{BCA}=30^\circ$ Ta có $\sin\widehat{BCA}=\frac{AB}{AC}=\frac{1}{2}$ $\Rightarrow BC=2\sqrt{3}~cm$ b) Ta có $\widehat{BDH}=\widehat{BAC}=60^\circ$ $\Rightarrow \cos\widehat{BDH}=\cos60^\circ=\frac{1}{2}$ Ta có $\widehat{DHC}=\widehat{BAC}=60^\circ$ $\Rightarrow \widehat{IDC}=\widehat{BDA}=30^\circ$ $\Rightarrow \widehat{DHC}=\widehat{BDA}$ Mà $\widehat{CDH}$ chung $\Rightarrow \Delta CDH\backsim \Delta ADB$ (g-g) $\Rightarrow \frac{DC}{AD}=\frac{DH}{DB}$ $\Rightarrow DB.DA=DH.DI$ c) Ta có $\widehat{DKH}=90^\circ$ $\Rightarrow DK=DH.\sin\widehat{DBK}$