Kẻ đường cao AD.
Có: DB=DC=\(\dfrac{4}{2}=2\left(cm\right)\)
Xét \(\Delta_vABD\), có: \(\cos ABC=\dfrac{BD}{AB}=\dfrac{2}{8}=\dfrac{1}{4}\)\(\Rightarrow\)\(\widehat{ABC}\approx76^o\)
Có: \(\Delta_vDBC=\Delta_vECB\left(ch-gn\right)\)(\(\widehat{ABC}=\widehat{ACB}\left(gt\right);BC\): chung)
\(\Rightarrow BD=CE=BC.\cos ABC=4.\cos76^o\)\(\approx0,97\left(cm\right)\)\(\Rightarrow AD=AE=8-0,97=7,03\left(cm\right)\)\(\Rightarrow\Delta ADE\) cân tại A.
Xét \(\Delta ADE\) và \(\Delta ABC\)\(\widehat{A}\)có: \(\widehat{A}\):chung.
\(\Rightarrow\Delta ADE\sim\Delta ABC\left(gn\right)\)
\(\Rightarrow\dfrac{AD}{AB}=\dfrac{DE}{BC}\)
hay: \(\dfrac{7,03}{8}=\dfrac{DE}{4}\Rightarrow DE=\dfrac{7,03.4}{8}=3,515\left(cm\right)\)
