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)