Final answer:
The problem relates to trigonometric functions and vector calculations within a geometrical context, tackling concepts of vector components and angles. Moreover, the Parallax method is referenced as a technique for estimating distances.
Step-by-step explanation:
The question is asking for a calculation related to vectors, angles, and distances in a geometrical context, with an emphasis on trigonometric functions and vector addition. To answer the student's question, one must apply trigonometric ratios and vector operations.
The mention of diagonal AC, vector BD, and angle BOC suggests a polygon, possibly a rectangle or a parallelogram, where trigonometric functions are used to find vector components and the Parallax method to approximate distances based on angles.
For example, the calculations Bx = B cos β and By = B sin β are used to find the horizontal (x) and vertical (y) components of vector B, using the cosine and sine functions respectively.
Similarly, Cx and Cy are the horizontal and vertical components of vector C. Angles are measured in degrees, and the negative sign indicates the direction of the vector component.
The Parallax method denotes a geometrical approximation used to estimate distances based on observational angles. This method generally involves creating congruent triangles and using basic proportional relationships to determine unknown distances. The examples provided within the question hint at the application of these principles.