Final answer:
Without additional context, it's impossible to determine the correct expression for the length of segment AC. However, in vector mathematics, the magnitude of a vector is typically related to its components through trigonometric identities such as cosine and sine for right triangles.
Step-by-step explanation:
The question asks which expression could be used to determine the length of segment AC. To answer this, we need more context regarding the relationship between the points and segments mentioned. However, by looking at the options provided and typical vector notation, we can surmise that the question likely involves vector operations or the use of trigonometry with right triangles. Commonly, in vector mathematics, the length of a vector can be determined by using its components and trigonometric relations.
Without additional information about the points A, B, C, Ax, and Ay, it's impossible to definitively choose one of the provided options. Nonetheless, if we assume Ax and Ay are the components of vector A on the x and y axes respectively, and AB is a magnitude of a vector from A to B, the use of trigonometric identities such as Ax = A cos θ and Ay = A sin θ might be relevant. These identities relate the components of a vector to its magnitude and the angle it makes with the x-axis in a right-angled triangle framework.
By applying trigonometric identities involving cosine and sine, we can sometimes express the magnitude of one vector in terms of the components or magnitudes of others, especially if the vectors form right-angled triangles on the plane or if we have information about the angles involved.