The assignment asks to "Compute for the Resultant of the forces $F = 450 \, \text{N}$" using three methods: Trigonometric Method, Graphical Method, and Component/Analytical Method.

Explanation:

This problem involves determining the resultant force when two or more forces act at an angle. Here's how to approach it with each method:

1. Trigonometric Method:

   • Use the Law of Sines or Cosines depending on the angles provided.
   • Decompose the forces into components and then use trigonometric identities to find the resultant.

2. Graphical Method:

   • Draw the forces to scale on graph paper.
   • Use the head-to-tail method to find the resultant force vector.
   • Measure the resultant's length and direction with a ruler and protractor.

3. Component/Analytical Method:

   • Break down each force into horizontal ($x$) and vertical ($y$) components.
   • Sum up the components separately.
   • Use Pythagorean theorem to find the magnitude of the resultant and inverse tangent to find the direction.

Do you want a step-by-step detailed solution for any of these methods?

Relative Questions:

1. How do you find the direction of the resultant force using trigonometry?
2. What are the advantages of using the graphical method for finding resultants?
3. How does breaking down forces into components simplify solving these types of problems?
4. Could the same approach be used if the forces were not coplanar? How?
5. What tools are typically used in the graphical method, and why?

Tip:

When solving for the resultant force, always double-check the angle's reference direction (e.g., from the horizontal or vertical) to ensure accuracy.