7.52 In a triangle, one side is twice another side, and one of the angles is $30^{\circ}$. Then this triangle
(A) must be a right triangle.
(B) must be an obtuse triangle.
(C) could be an acute triangle.
(D) none of the above conclusions is correct.
(Shanghai Junior High School Mathematics Competition, 1984)
[Solution] In $\triangle ABC$, let $a=2, b=1$.
(1) If $\angle A=30^{\circ}$,
$\because b<120^{\circ}$, i.e., $\triangle ABC$ is an obtuse triangle, then (A) is false.
(2) If $\angle B=30^{\circ}$, by $\frac{a}{\sin A}=\frac{b}{\sin B}$, we get $\sin A=1$, so $\angle A=90^{\circ}$. Thus, (B) is false.
(3) If $\angle C=30^{\circ}$, by the cosine rule, we can find $c>b$, hence $\angle B<120^{\circ}$.
In summary, $\triangle ABC$ cannot be an acute triangle. Therefore, (C) is false. Hence, the answer is (D).