This should be an arc length problem. Imagine the motion of the swing forming a sector of arclength s and radius r, where the radius is from the pivot point to the seat. Let r = 8 feet and let s, the arc subtended, be 9.5 feet. The arclength formula is s = rθ, where θ is in radians. So, θ = s/r = (9.5 feet) / (8 feet) = 1.19 rad.
We can convert this answer to degrees by θ = 1.19 rad*(180 deg / π rad) = 68.2 deg