Final answer:
To find the magnitude and direction of the resultant force, use the Pythagorean theorem on the horizontal and vertical components, and measure the angle relative to a reference axis, using trigonometric functions for analytical precision.
Step-by-step explanation:
To determine the magnitude and coordinate direction angles of the resultant force, you must first resolve the force into its horizontal and vertical components, often labeled as Ax and Ay. Once these components are established, the magnitude of the resultant vector, denoted as R, can be found using the Pythagorean theorem. This is calculated as the square root of the sum of the squares of Ax and Ay.
To find the direction of the resultant vector, you should measure its angle in relation to a reference axis. Typically, this is the horizontal (x-axis) or the vertical (y-axis). The direction of R is measured using a protractor. If the resultant vector is below the horizontal, as it is south of the eastward axis, turn the protractor upside down to measure the angle correctly.
In practice with actual vectors drawn to scale, a ruler and protractor can be used to visually measure these values. However, in analytical or computational scenarios, appropriate trigonometric functions such as the tangent function are applied to find the angle based on Ax and Ay components.