A midpoint in a right triangle

Core stretch

In \(\triangle ABC\), \(D\) is the midpoint of \(AC\), \(BD\perp AC\), \(AB=25\) cm, and \(\sin\angle BAD=3/5\). Find

1. \(AC\),[2]
2. \(\tan\angle ABD\),[2]
3. the shortest distance from \(A\) to the line \(BC\), produced if necessary.[2]