Final answer:
Given side a=10, side b=40, and angle A=30°, only one triangle can be formed. This conclusion is drawn using the Law of Sines and the relations between the sides and angles of a triangle.
Step-by-step explanation:
Determining the Number of Possible Triangles
When attempting to determine the number of triangles that can be formed given side a=10, side b=40, and angle A=30°, we must consider the Law of Sines which states:
a/sin A = b/sin B
In this case, we can find the potential values for angle B and subsequently determine the possible shape(s) of the triangle. However, due to the specific measures given, there is only one unique solution for the triangle. This is because the angle A is already the smallest angle being opposite the smallest side. The side b is too large compared to side a for there to be an ambiguous case, which typically occurs when the given side opposite the given angle is the longest side, or we have a case where two different angles could potentially work. Therefore, only one triangle can be formed with the given measurements.