2. In $\triangle A B C$, one side is half of another, and one of the angles is $30^{\circ}$. Then the shape of this triangle is ( ).
(A) not a right triangle
(B) not an obtuse triangle
(C) not an acute triangle
(D) any of the above is possible
2. C.

Let the three sides of the triangle be $a, 2a, b$. Clearly, the side opposite the $30^{\circ}$ angle is not the longest side.
(1) If the side opposite the $30^{\circ}$ angle is $a$, then the angle opposite $2a$ is $90^{\circ}$, making $\triangle ABC$ a right triangle;
(2) If the side opposite the $30^{\circ}$ angle is $2a$, then the angle opposite $a$ is less than $30^{\circ}$, and thus the angle opposite $b$ is greater than $120^{\circ}$, making $\triangle ABC$ an obtuse triangle;
(3) If the side opposite the $30^{\circ}$ angle is $b$, then by $a+b>2a$ we know $b>a$, so the angle opposite $a$ is less than $30^{\circ}$. Thus, the angle opposite $2a$ is greater than $120^{\circ}$, making $\triangle ABC$ an obtuse triangle.
Therefore, in all three cases, the triangle is not an acute triangle.