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The image contains a problem related to calculating the resultant force of several forces with given magnitudes, angles, and coordinates.

### Given forces:
1. \( F_1 = 3 \, \text{ton}, \, \alpha_1 = 45^\circ \), coordinates: \( (0, 4) \)
2. \( F_2 = 2 \, \text{ton}, \, \alpha_2 = 19^\circ \), coordinates: \( (4, 9) \)
3. \( F_3 = 4 \, \text{ton}, \, \alpha_3 = 27^\circ \), coordinates: \( (9, 7) \)
4. \( F_4 = 8 \, \text{ton}, \, \alpha_4 = 14^\circ \), coordinates: \( (21, 16) \)

### Tasks:
Find the resultant force using:
- (a) Parallelogram method (graphical)
- (b) Polygon of forces (graphical)
- (c) Analytical method

Would you like to delve into the analytical method first? Or would you prefer guidance on graphical solutions?

### Related questions:
1. What are the vector components of each force?
2. How is the resultant force calculated using the parallelogram method?
3. What is the process for resolving forces graphically?
4. How do you find the magnitude and direction of the resultant force analytically?
5. How do angles affect the resolution of forces?

**Tip:** When resolving forces, always break them into horizontal and vertical components for ultimate accuracy.

F1 = 3 ton with α1 = 45° at coordinates (0,4), F2 = 2 ton with α2 = 19° at coordinates (4,9), F3 = 4 ton with α3 = 27° at coordinates (9,7), and F4 = 8 ton with α4 = 14° at coordinates (21,16). Find the resultant force using: (a) Parallelogram method (graphical), (b) Polygon of forces (graphical), and (c) Analytical method.

Learn how to calculate the resultant force from multiple forces given by their magnitudes, angles, and coordinates. This guide covers the graphical (parallelogram and polygon) and analytical methods for solving resultant forces, including vector resolution into components and using the Pythagorean theorem. Suitable for physics and engineering students.

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