The answer is as follows:

Pass point b as the vertical line of AC. Then the BC length obtained at this time is the shortest Because according to junior high school knowledge, take any other point on AC, such as point C 1 and BCC 1 to form a right triangle, where BC is the right-angled side and BC 1 is the hypotenuse, and the length of the hypotenuse in the right-angled triangle in junior high school knowledge is longer than the right-angled side, so BC is the shortest when it is vertical, because it is true for any other point on AC.

According to the knowledge of Grade One, the right-angled side opposite the 30-degree angle is equal to half of the hypotenuse, AC=4, so BC=2.

Finally, the range of BC is that the length of BC is greater than or equal to 2.

Since you can't write a triangle diagram in the post, please draw a diagram according to my reasoning, which is easier to understand. It's all your knowledge in the first year of high school.