Answer:
A, C, E
Explanation:
remember to law of sine :
a/sin(A) = b/sin(B) = c/sin(C)
or the "upside-down" version :
sin(A)/a = sin(B)/b = sin(C)/c
with a, b, c being the sides of the triangle, and A, B, C being the corresponding opposite angles in the triangle.
so, as you can clearly see, we always need at least one angle and one side (in fact either 2 angles one side or 1 angle 2 sides) to use the law of sine to solve the rest of the triangle.
therefore, the answer options A, C, E are correct.
for SSS (all 3 sides are known) we need the law of cosine to solve the angles (at least one of them, and then we could continue with either law).
remember :
c² = a² + b² - 2ab×cos(C)
again, a,b,c are the sides, and C is the opposite angle of whatever side we define as "c".
that's why I always call this the extended Pythagoras.
for AAA (all 3 angles are known) we cannot solve the triangle, because dilated triangles all have the same angles. and therefore there are infinitely many triangles with the same angles.