1. A point on the ceiling of a room is 12ft. from each of the vertices of a triangle on the floor whose legs are 6ft. A and 8ft. respectively. find the length of the ceiling.
2. With a 12ft. pole marked in feet, how can one determine the foot of the perpendicular let fall to the floor from a point on a ceiling of a room 9ft. high?
3. A hill slopes down from a building with a grade of one for to five feet measured along the horizontal (slope of 1/5). If a ladder 36 ft. long is set against the building, with its foot 12ft. down the hill. How high will it reach the building?