Question

Answer 1

Xét ΔADB vuông tại D có

\(sinBAD=\dfrac{BD}{AB}\)

=>\(\dfrac{BD}{6}=sin60=\dfrac{\sqrt{3}}{2}\)

=>\(BD=3\sqrt{3}\left(cm\right)\)

ΔADB vuông tại D

=>\(DA^2+DB^2=AB^2\)

=>\(DA^2=6^2-27=9\)

=>DA=3(cm)

Xét ΔABC có

\(cosBAC=\dfrac{AB^2+AC^2-BC^2}{2\cdot AB\cdot AC}\)

\(\Leftrightarrow cos60=\dfrac{6^2+7^2-BC^2}{2\cdot6\cdot7}\)

=>\(36+49-BC^2=2\cdot6\cdot7\cdot\dfrac{1}{2}=42\)

=>\(BC^2=36+49-42=43\)

=>\(BC=\sqrt{43}\left(cm\right)\)