令,BD:DC:DA=2:3:6=2m:3m:6m,
则有,
BD=2m,CD=3m,AD=6m.
AB^2=AD^2+BD^2=40m^2,
AC^2=AD^2+CD^2=45m^2.
cos角BAC=(AB^2+AC^2-BC^2)/(2AB*AC)=√2/2=cos45,
则,角BAC=45度.