I believe you have the 34° angle in the wrong place.
1. A pole 60 feet tall is situated at the bottom of a hill that slopes up at an angle of 15.9°.
A guy wire from the top of the pole to the hillside forms an angle of 34° with the top of the pole.
Find the distance from the base of the pole to the guy wire's point of attachment.
60 | \
| \ *
| \ C *
| 71.9° o
| 74.1° *
| * 15.9°
B o - - - - - - - - - - - - - - - D
The pole is:
The ground is
The guy wire is
Law of Sines: . etc.