Question 964121
Let A represent the center of the circle.  Let the point B be a point at the intersection of the one end of the chord and the edge of the circle.  Finally, let C represent a point between the center of the circle and the midpoint of the cord.  The triangle ABC is a right triangle with a 90 degree angle at ACB.  Since the cord length is 30, the bisected segment BC is length 15 .
(length AB)^2 = (length BC)^2 + (length AC)^2
17^2 = 15^2 + (length AC)^2
289 = 225 + (length AC)^2
add -225 to each side
 64 = (length AC)^2
take square root of each side
 8 = length AC