Final answer:
To calculate the magnitude of the sum of two vectors, one must first resolve the vectors into their x and y components, add these components, and use the Pythagorean theorem. However, the question lacks sufficient details to provide an exact numerical answer.
Step-by-step explanation:
The question appears to be asking for the magnitude of the sum of two vectors, which falls under the subject of Physics, specifically vector addition, a concept often covered in high school curricula. To find the sum of the two vectors, we need to break each vector down into its x and y components, add them together, and then use the Pythagorean theorem to find the resultant vector's magnitude.
However, the question does not provide enough information because the vectors' magnitudes and directions are not sufficiently specified. Assuming the vectors provided in the question (16.3 m at 27.8° and 7.70 m at 20.0°) are correct and need to be summed, one could perform the following calculations:
- Resolve each vector into its horizontal (x) and vertical (y) components.
- Add the respective components together to get the resultant components.
- Calculate the magnitude of the resultant vector using the Pythagorean theorem: R = √(Rx² + Ry²).
Using the correct values for the vectors' magnitudes and angles, a specific numerical answer can be provided if the vectors are correctly stated.