Question

In which case(s) of given information can solving the triangle result in two possible triangles?

Select all that apply

SSS

SSA

SAS

ASA

AAS

Answer 1

Only SSA.

Reason: SSA (two sides and a non‑included angle) is the classic "ambiguous case" for the Law of Sines — depending on the given lengths and the given angle there can be 0, 1 or 2 distinct triangles. (Geometric description: if a is the side opposite the given angle A, b the other known side, and h = b·sinA, then if a<h no triangle, a=h one right triangle, h<a<b two triangles, and a≥b one triangle.)

SSS, SAS, ASA and AAS determine a triangle uniquely (up to congruence), so they do not produce two possible triangles.