60.  To  compute  the  horizontal  distance  between  two  inac-
cessible points  A  and  B,  when  no  point  can  be  found  whence
both  can  be  seen.  Take  two  points  C  and  D,  distant  200  yds.,
so  that  A  can  be  seen  from  C,  and  B  from  D.  From  C  meas-
ure CF,  200  yds.  to  F,  whence  A  can  be  seen ;  and  from  D
measure  DF,  200  yds.  to  F,  whence  B  can  be  seen.  Measure
AFC,  83°;  ACD,  53°  30';  ACF,  54°  31';  BDF,  54°  30';
BDC,  156°  25';  DFB,  88°  30'.
61.  A  column  in  the  north  temperate  zone  is  east-southeast
of  an  observer,  and  at  noon  the  extremity  of  its  shadow  is
northeast  of  him.  The  shadow  is  80  ft.  in  length,  and  the
elevation  of  the  column,  at  the  observer's  station,  is  45°.
Find  the  height  of  the  column.
62.  From  the  top  of  a  hill  the  angles  of  depression  of  two
objects  situated  in  the  horizontal  plane  of  the  base  of  the  hill
are  45°  and  30° ;  and  the  horizontal  angle  between  the  two
objects  is  30°.  Show  that  the  height  of  the  hill  is  equal  to
the  distance  between  the  objects.
63.  Wishing  to  know  the  breadth  of  a  river  from  A  to  B,
I  take  AC,  100  yds.  in  the  prolongation  of  BA,  and  then  take
CD,  200  yds.  at  right  angles  to  AC.  The  angle  BDA  is  37°
18'  30".     Find  AB.
64.  The  sum  of  the  sides  of  a  triangle  is  100.  The  angle
at  A  is  double  that  of  B,  and  the  angle  at  B  is  double  that  at
C.     Determine  the  sides.
MISCELLANEOUS   EXAMPLES.  91

65.  If  sin^A  -f  5  cos^^  =  3,  find  A.
66.  If  sinM  =  m  cos  A  —  n,  find  cos  A.
