Final answer:
To determine the direction of the sum of the two vectors, we use the analytical method to break each vector down into x and y components, and then add these components to find the resultant vector's magnitude and direction.
Step-by-step explanation:
To find the direction of the sum of two vectors, we can use the analytical method which involves breaking down the vectors into their components, and then combining the components to find the resultant vector's magnitude and direction. We will use trigonometry for the vectors given in the problem. Each vector can be broken into an x (horizontal) component and a y (vertical) component.
For example, Vector A with a magnitude of 16.3 m at 20.0° can be broken down into Ax = 16.3 m * cos(20.0°) and Ay = 16.3 m * sin(20.0°). Similarly, Vector B with a magnitude of 7.70 m at 27.8° can be broken down into Bx = 7.70 m * cos(27.8°) and By = 7.70 m * sin(27.8°). To find the resultant vector, R, we add the x-components together and y-components together.