Answer
$C$ and $D$ provides insufficient information.
Work Step by Step
Law of sines:
For a triangle $ABC$ with sides $a, b, c$:
$$\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$$
Now, look at the image of the triangle below.
A. 2 angles and the side included between them are given.
For example, in the image, angles $B$ and $C$ and side $a$ are given.
As 2 angles are given, we can figure out the angle $A$ according to the fact that $$\angle A+\angle B+\angle C=180^\circ$$
Therefore, $\sin A$, $\sin B$ and $\sin C$ and side $a$ are known.
From law of sines: $$\frac{a}{\sin A}=\frac{b}{\sin B}$$
$b$ can be calculated.
$$\frac{a}{\sin A}=\frac{c}{\sin C}$$
$c$ can be calculated.
Therefore $A$ provides sufficient information.
B. 2 angles and a side opposite one of them are given.
For example, in the image, angles $B$ and $C$ and side $b$ are given.
Again, as 2 angles are given, we can figure out the angle $A$ according to the fact that $$\angle A+\angle B+\angle C=180^\circ$$
Therefore, $\sin A$, $\sin B$ and $\sin C$ and side $b$ are known.
From law of sines: $$\frac{a}{\sin A}=\frac{b}{\sin B}$$
$a$ can be calculated.
$$\frac{b}{\sin B}=\frac{c}{\sin C}$$
$c$ can be calculated.
Therefore $B$ provides sufficient information.
C. 2 sides and an angle between them are given.
For example, in the image, sides $b$ and $c$ and angle $A$ are given.
Unfortunately, knowing $b$ and $c$ does not help us to find out $a$.
Therefore, it is not enough to find out all other 3 unknown elements.
$C$ provides insufficient information.
D. 3 sides are given.
In the image, $a, b, c$ are given.
Here 3 sides are given. However, in the law of sines, 3 sides are all in the numerators, with all unknowns in the denominator. That means we cannot figure out the unknown ones.
$D$ also gives out insufficient information.
