Final answer:
A vector can indeed form a right-angle triangle with its components, and it's true that the Pythagorean theorem can be used to calculate a resultant vector. However, the question about the centroid is incomplete without additional information about the shape.
Step-by-step explanation:
The question is related to the concept of centroids in plane figures, vector operations, and properties of geometric shapes. Unfortunately,, as the location of the centroid depends on the specific shape and dimensions, not just area A=15 in2. When finding a centroid, this requires knowing the shape or at least having a density function provided. For vectors, it's true that a vector can form a right-angle triangle with its components on the x and y axes. This is due to the vector's ability to be broken down into orthogonal components, where the Pythagorean theorem can be applied. Furthermore, when adding two vectors at right angles, you can calculate the length of the resultant vector using the Pythagorean theorem as well.
For example, assuming we have two perpendicular vectors A and B, with lengths a and b, respectively. The resultant vector R, which is the diagonal of the formed rectangle, will have a length calculated by R = √(a2 + b2). This calculation is perfect for scenarios where you're finding a resultant vector in physics or resolving forces in engineering.