Final answer:
The vector A is resolved into x- and y-components using trigonometry based on its magnitude and angle θ. Vector addition involves calculating these components for each vector and then using the Pythagorean theorem and trigonometry to find the resultant vector's magnitude and direction.
Step-by-step explanation:
To find the value of vector A and the angle measures of a polygon, we use the component method to resolve the vector into its x- and y-components. Given that the magnitude of vector A is known and it forms an angle θ with the reference frame, we can calculate the components using the cosine and sine functions respectively. The x-component Ax is found by Ax = A cos θ.
For the specific problem of finding the addition of two vectors A and B with their respective magnitudes and directions specified, we first calculate their components along the x- and y-axis. Then using these components, we apply the Pythagorean theorem and trigonometric relationships to obtain the magnitude and direction of the resultant vector.