In a circle, the angle subtended by a chord at the circumference is half the angle subtended by the same chord at the center of the circle.
In this problem, the chord is 3 cm from the center of the circle, so it divides the diameter of the circle into two parts: one of length 3 cm and the other of length 2 × 14 - 3 = 25 cm. Using the Pythagorean theorem, we can find that the distance from the midpoint of the chord to the center of the circle is √(14² - 1.5²) = √195.25 ≈ 13.98 cm.
Therefore, the angle subtended by the chord at the center of the circle is 2 tan^(-1)(1.5/13.98) ≈ 0.215 radians.
The angle subtended by the chord at the circumference of the circle is half this angle, which is approximately 0.108 radians. To convert this to degrees, we multiply by 180/π:
0.108 radians × 180/π ≈ 6.17 degrees
So the angle subtended by the chord at the circumference of the circle is approximately 6.17 degrees.