Xét ΔANB vuông tại N ta có:
\(tanABC=\dfrac{AN}{BN}=>BN=\dfrac{AN}{tanABC}=\dfrac{AN}{tan38^o}\)
Xét ΔANC vuông tại N ta có:
\(tanACB=\dfrac{AN}{CN}=>CN=\dfrac{AN}{tanACB}=\dfrac{AN}{tan30^o}\)
Ta có: \(BC=CN+BN=11=>\dfrac{AN}{tan38^o}+\dfrac{AN}{tan30^o}=11\)
\(=>AN\left(\dfrac{1}{tan38^o}+\dfrac{1}{tan30^o}\right)=11\\ =>3AN=11\\=>AN=\dfrac{11}{3}\left(cm\right) \)