Please help me with this trigonometry problem regarding the sine law.?

64degree

Ok first you must clarify.  Is the hillside 27 meters long or the shadow on the hill side.  If the hill side is say 10 meters tall and the shadow is 27 meters then the shadow is 17 meters longer than the hill.  We would have a hard time figuring this out if that was the case because the shadow bends.  We would need to straighten the shadow out somehow.  We'd need to dig a hole so that the shadow fell all 27 meters at the same angle as the hill.  Which is another thing that you don't tell us, what is the angle of the hill.  Conversely, what if the hill was 100 meters tall, then all we would need to estimate is the angle of the hill and then we could figure the problem easy.  

http://upload.wikimedia.org/math/3/8/1/3814ef0ec01bf92e5ecff3d92a9d0b3d.png