Final answer:
To find the measure of an angle in vector problems, calculate the x- and y-components using trigonometric functions and apply vector addition or subtraction principles as needed.
Step-by-step explanation:
To solve for the measure of angle A or any other questions involving vector components, we follow the analytical approach of breaking vectors into their x- and y-components. If given vectors A and B with their magnitudes and angles, we can find their x-components Ax and Bx using the cosine of their respective angles (cos 0). The formula Ax = A * cos(0) allows us to calculate the x-component of vector A, which in the context of a vector addition or subtraction problem, contributes to finding the resultant vector's magnitude and direction.
For challenges like finding the angle between two vectors given their magnitudes and the magnitudes of their sum and difference, or fencing off a plot of land and needing to compute the length and orientation of the fourth side, the principles of vector addition, subtraction, and trigonometry come into play.