Let AD and BC be two vertical poles
at A and B respectively on a horizontal ground.
If AD = 8 m, BC = 11 m and AB = 10 m; then the distance
(in meters) of a point M on AB from the point A such
that MD² + MC² is minimum is ______.

The angle of elevation of the top of a hill from a point on the horizontal plane passing through the foot of the hill is found to be 45^o. After walking a distance of 80 meters towards the top, up a slope inclined at an angle of 30^o to the horizontal plane, the angle of elevation of the top of the hill becomes 75^o. Then the height of the hill (in meters) is ____________.