Final answer:
Given the conditions a=13, b=6, and c=6 degrees, no triangle can be formed. This is because, according to the triangle inequality theorem and law of sines, the longest side cannot lie opposite the smallest angle, which contradicts the given lengths.
Step-by-step explanation:
The question asks about the number of triangles that can be formed given the conditions a=13, b=6, and c=6 degrees.
To determine the number of possible triangles, we need to interpret the 'c' value correctly, as it denotes an angle measurement, not a side length. Commonly, the notation for sides is lowercase (a, b, c), while angles are denoted by uppercase letters (A, B, C). Assuming that 'c' is a typo and should be an angle 'C', we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side.
Given sides 'a' and 'b', and assuming 'c' refers to an angle 'C' with a degree of 6, we can immediately see that the provided lengths of 13 and 6 satisfy the triangle inequality theorem (13 < 6 + 6). However, since we are given an angle that is extremely small (6 degrees), we must consider whether it is possible to form a triangle with two sides of the same length (6 units each) and a markedly longer side (13 units).
Using the law of sines, we can write a/sin A = b/sin B = c/sin C, it becomes clear that, for any angle C that is significantly smaller than the angles at the base of an isosceles triangle (which is what we would have if the two sides b and c were equal), the side opposite the smaller angle (side a) must be the smallest side, which contradicts our given condition that a is the longest side (13 units).
Therefore, it is not possible to form a triangle with the given conditions, and the answer is A. 0.