It's actually both C and D, although I wouldn't be surprised if your
teacher or book author says the law of cosines cannot be used for SSA.
If they do, they're wrong!

It's not normally used for SSA but it can be used.  Below is
proof that the SSA case can be solved completely using the
law of cosines only, and not using the law of sines at all.

The law of cosines can be stated any of these three ways:

1.  a² = b² + c² -2bc cos(A)
2.  b² = a² + c² -2ac cos(B)
3.  c² = a² + b² -2ab cos(C)

Suppose a=8, c=7, C = 60°

Use form 3:

c² = a² + b² -2ab cos(C)
7² = 8² + b² - 2(8)(b)cos(60°)
49 = 64 + b² - 2(8)(b)(1/2)
49 = 64 + b² - 8b
 0 = b² - 8b + 15
 0 = (b - 5)(b - 3)
     b - 5 = 0;  b - 3 = 0
         b = 5;      b = 3

Then for b = 5 use the law of cosines form 1

a² = b² + c² -2bc cos(A)
8² = 5² + 7² -2(5)(7) cos(A)
64 = 25 + 49 - 70cos(A)
64 = 74 - 70cos(A)
-10 = -70cos(A)
1/7 = cos(A)
81.8° = A

Then find the third angle by adding 
angle B by adding A and C and subtracting 
from 180°

81.8° + 60° = 141.8°
180° - 141.8° = 38.2°

So we solved the SSA case completely by
the law of cosines, without using the law of 
sines at all.

This was an ambiguous case and we can solve for
the other solution the same way, using b = 5.

So the law of cosines can be used for the SSA case.

Edwin