Ban tu ve hinh nha
( tam giac ABC vuong tai A , duong cao AH)
Xet tam giac HAB va tam giac HCA Co
\(\hept{\begin{cases}\widehat{AHB}=\widehat{CHA}=90\\\widehat{HBA}=\widehat{HAC}\left(phu\widehat{HAB}\right)\end{cases}=>\Delta HAB}\) dong dang voi \(\Delta HCA\left(G-G\right)\)
Suy ra\(\frac{AB}{AC}=\frac{HB}{HA}=\frac{HA}{HC}=\frac{4}{9}\left(gt\right)\) =>\(HB=\frac{4HA}{9},HC=\frac{9HA}{4}\)
=>\(\frac{HB}{HA}=\frac{\frac{4HA}{9}}{\frac{9HA}{4}}=\frac{4HA}{9}.\frac{4}{9HA}=\frac{16}{81}\)
Suy ra ti so hinh chieu cua hai canh goc vuong do tren canh huyen =16/81
Chuc ban hoc tot