When the angle of elevation of the sun in 64 a telegraph pale that in tilted at an angle of 12 directly away from the sun casts a shadow 34 feet long on level ground. What is the length of the pole?

##49.6## feet
Here is what I assume is the arrangement:
##/_CAB=90^@-12^@=78^@##
##rArr /_ACB= 180^@-(78^@+64^@)=38^@##
By :
##color(white)(XXX)(|AC|)/(sin(64^@)) = (32 feet)/(sin(38^@))##
Therefore
##color(white)(XXX)|AC| = 32 feet xx sin(64^@)/sin(38^@)##
##color(white)(XXXXXX)~~ 49.6 feet## according to my calculator)