Final answer:
To find the resultant force of the two given forces, break down each force into its x and y components using trigonometry, add the x and y components separately, find the magnitude of the resultant force using the Pythagorean theorem, and determine the direction using the inverse tangent function.
Step-by-step explanation:
To find the resultant force of the two given forces, we need to add the forces as vectors. We can break down each force into its x and y components using trigonometry. For F₁, the northward component is given by 53.89 * sin(75°) = 51.92 N and the westward component is -53.89 * cos(75°) = -16.34 N. For F₂, the southward component is given by 95.72 * sin(143°) = -86.45 N and the westward component is -95.72 * cos(143°) = -40.10 N.
Adding the x components and y components separately:
Sum of x components = -16.34 N - 40.10 N = -56.44 N
Sum of y components = 51.92 N - 86.45 N = -34.53 N
The resultant force is the vector sum of the x and y components, which can be found using the Pythagorean theorem:
Resultant force = sqrt[(-56.44 N)^2 + (-34.53 N)^2] = 66.90 N
The direction of the resultant force can be found using the inverse tangent function:
Direction = atan(-34.53 N / -56.44 N) = 33.60°
Therefore, the resultant force is 66.90 N, 33.60° south of west.