Question

Answer 1

Do \(AB=AC\Rightarrow\Delta ABC\) cân tại A \(\Rightarrow\widehat{B}=\widehat{C}\)

Mặt khác \(\left\{{}\begin{matrix}BC>AB\\BC>AC\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}\widehat{A}>\widehat{B}\\\widehat{A}>\widehat{C}\end{matrix}\right.\) (trong tam giác, góc đối diện với cạnh lớn hơn thì lớn hơn)

\(\Rightarrow2\widehat{A}>\widehat{B}+\widehat{C}\)

\(\Rightarrow3\widehat{A}>\widehat{A}+\widehat{B}+\widehat{C}=180^0\)

\(\Rightarrow\widehat{A}>60^0\)

Lại có: \(180^0=\widehat{A}+\widehat{B}+\widehat{C}=\widehat{A}+2\widehat{B}>\widehat{B}+2\widehat{B}=3\widehat{B}\)

\(\Rightarrow\widehat{B}< 60^0\)

Vậy \(\widehat{A}>60^0>\widehat{B}\)