Answer:
30 in
Step-by-step explanation:
See attached image.
The length of AB is 17 (radius). The length of AC is 8 (given info).
AC splits segment BD in half, so point C is the midpoint of segment BD.
AC is perpendicular to the chord, so triangle ABC is a right triangle. You now have a right triangle with a leg of length 8 and hypotenuse of lenght 17.
The Pythagorean Theorem: (leg)^2 + (leg)^2 = (hypotenuse)^2.
[tex]8^2+(BC)^2=17^2\\\\64+(BC)^2=289\\\\(BC)^2=225\\\\BC=\sqrt{225}=15[/tex]
That's half the length of the chord, so double that to get 30 inches for the full length of the chord BD.
