The question shows a right angle triangle where the opposite side is unknown. There is a line drawn from one corner of the triangle which makes another triangle within the right angle triangle, the hypotenuse is a common side of both triangles, part of the adjacent side is common to both triangles and the opposite side is exclusive to the right angle triangle. The sine rule is used to find the length of the hypotenuse, which in turn is used to find the length of the opposite side. I hope that's not too confusing, a picture would be much easier.
h/sin(135) = 50/sin(15)
hsin(15) = 50sin(135)
h = 50sin(135)/sin(15)
h = 136.6025404 (hypotenuse)
136.6025404sin(30) = 68.30127019 (opposite side length)
Having said all that I suspect my teacher has simply made a mistake. I'll send her an email and ask her to check it again, hopefully she'll have time.