[net.puzzle] Ladder problem

lief@hpfcrs.UUCP (lief) (10/12/84)

         |X|                      This puzzle is very straight forward:
___      |X|    ___
 |       |X|\\    \               Given a 12 foot ladder on the floor leaning
 |       |X| \\    \              against a wall with the corner of a 4 foot
 |       |X|  \\    \             square box touching the ladder as in the
 |       |X|   \\    \            diagram.
 |       |X|    \\    \
 h       |X|     \\   12ft        Problem:  *WITHOUT USING CALCULUS* find the
 |       |X|      \\    \         value of h (height of wall where top of
 |  ___  |X|_______\\    \        ladder is resting).
 |   |   |X|       |\\    \
 |  4ft  |X|       | \\    \      Lief Sorensen
_|_ _|_  |X|_______|  \\   _\_    Hewlett Packard Co.
================================= 
           |- 4ft -|

P.S.  After solving the above, for extra credit replace the 4 foot box with
      a 2 foot radius ball.  With the ladder touching the ball, solve the
      problem as above.