Final answer:
To calculate the component of a force of 200 N at a direction of 60°, the horizontal component (using cosine) is 100 N and the vertical component (using sine) is approximately 173.2 N.
Step-by-step explanation:
To calculate the component of a force of 200 N at a direction of 60° to the force, we can use trigonometric relationships. The horizontal component of the force can be found using cosine, and the vertical component using sine, as these components are the adjacent and opposite sides of a right triangle formed by the force vector.
In this case, the horizontal component (Fx) is calculated as 200 N × cos(60°), and the vertical component (Fy) as 200 N × sin(60°).
Substituting the values:
- Fx = 200 N × cos(60°) = 200 N × 0.5 = 100.0 N
- Fy = 200 N × sin(60°) = 200 N × √3/2 ≈ 173.2 N
Therefore, the components of the force are 100.0 N horizontally and approximately 173.2 N vertically.