Final answer:
The question is from high school level physics and involves finding the magnitude of a force vector and the angle it makes with the vertical, using vector components and trigonometric functions.
Step-by-step explanation:
The subject of the question relates to a physics concept involving forces and their impact on a dog during a walk. Specifically, the scenario describes forces acting upon a dog named Fido being walked on a leash and includes calculation of magnitudes and angles of these forces based on given components. When solving for the magnitude of a force given its vector components, one uses the vector magnitude formula which is the square root of the sum of the squares of its components. To answer part (a), the magnitude of the pulling force F is calculated using the square root of the sum of the squares of the vector components:
Magnitude = \(\sqrt{98.0^2 + 132.0^2 + 32.0^2}\) Newtons.
To find the angle with the vertical for part (b), it is necessary to use trigonometric functions, considering only the vertical and horizontal components (ignoring the K - axial component as it doesn't affect the angle in the vertical plane).