Maths 1

A plank is used to reach over a fence 8ft high to support a wall that is 1 ft behind the fence (Figure A1). What is the length of the shortest plank that can be used? Lenght of plank  x  y 8 1 8 sin   ,  x csc x Hence, x  8 csc cos   1 1 1 ,  y sec  y Hence, y  1sec  L  x  y  8 csc   1sec  dL  8 csc  cot   1sec  tan  d   8  cos    1  sin         sin   sin    cos   cos     8 cos 3   sin 3  sin 2  cos 2  dL 0 d  8 cos 3   sin 3  0 sin 2  cos 2  0  8 cos 3   sin 3  For minimum, 8 cos 3   sin 3  8  tan 3  2