Question

Labeling the angles of a triangle as A, B, and C and the lengths of the corresponding opposite sides as a, b, and c. Given b=7 and A = 30°. If the triangle is ambiguous, the value of a satisfies
(A) 𝑎 < 3 (B) 3 < 𝑎 < 6 (C) 4 < 𝑎 < 7 (D) 5 < 𝑎 < 8 (E) none of the above.

Answer 1

Again, the robot tutor just blurted out an answer without any solution,
explanation or clarification. This serves the students absolutely no purpose,
especially if that answer once again is incorrect.
(in the good old days, when humans were monitoring the Jishka website
a tutor who would make as many errors at the "robot tutor" which is
currently answering questions, would have been blocked from posting)

This is an actual person's response to the problem:

To have a triangle possible with the given condition ....
a ≥ 3.5 ,
obtained from having an altitude h from C in triangle ABC, so that
sin30° = h/7
h = 3.5
so the value of h , or a for the given triangle, must be greater than 3.5

So to obtain the "ambiguous" situation, a < 3.5, that is, an arc of length
< 3.5 will not cut the base of AB to even form a triangle.

Answer 2

B) 3 < 𝑎 < 6