Final answer:
To find x and measure angles in vector component problems, one must identify the known vector magnitudes and angles, calculate the x- and y-components using trigonometric functions, and check if the results are reasonable.
Step-by-step explanation:
To find the value of x and then use it to find the measure of the angles, we need to work step-by-step through the given problem, which is based on vector components and trigonometric relationships in physics. The process involves identifying the known values for the vectors, such as magnitude and direction, and then using trigonometric functions to find the components of these vectors along the designated x- and y-axes.
Step 1 involves identifying the x- and y-axes and the components of each vector along these axes using the equations: Ax = A cos ϴ and Ay = A sin ϴ, where 'A' is the magnitude of the vector and 'ϴ' is the angle it makes with the x-axis.
In the problem, A = 53.0 m, angle A = 20.0°, B = 34.0 m, and angle B = 63.0°. After calculating the x-components using Ax = A cos ϴ, we can then apply the same process for the y-components. Once we find these components, we can add them to get the resultant vector's components. Lastly, checking the answer to ensure it is reasonable is an essential step.