Questions: Compute the vertical and horizontal components for each of the forces shown.

Solution Steps

• For (a): Force = 600 lb, Angle = 30°
• For (b): Force = 5 kips (5000 lb), Angle = 45°
• For (c): Force = 1200 lb, Angle = 30°

• Horizontal component \( F_x \) = \( F \cos(\theta) \) \[ F_x = 600 \cos(30°) = 600 \times \frac{\sqrt{3}}{2} = 600 \times 0.866 = 519.6 \text{ lb} \]
• Vertical component \( F_y \) = \( F \sin(\theta) \) \[ F_y = 600 \sin(30°) = 600 \times \frac{1}{2} = 600 \times 0.5 = 300 \text{ lb} \]

• Horizontal component \( F_x \) = \( F \cos(\theta) \) \[ F_x = 5000 \cos(45°) = 5000 \times \frac{\sqrt{2}}{2} = 5000 \times 0.707 = 3535 \text{ lb} \]
• Vertical component \( F_y \) = \( F \sin(\theta) \) \[ F_y = 5000 \sin(45°) = 5000 \times \frac{\sqrt{2}}{2} = 5000 \times 0.707 = 3535 \text{ lb} \]

Final Answer