A force of magnitude F is inclined at an angle θ to a given reference line. The normal (perpendicular) component of the force relative to that line equals:

Introduction / Context:
Resolving a force into components along and normal to a reference direction is a basic operation in statics and dynamics. Correct trigonometric association with the angle is essential for accurate equilibrium and motion analyses.

Given Data / Assumptions:

• A single force F making angle θ with the normal direction (or equivalently θ with the force's line to the reference axis).
• Right-triangle decomposition applies.
• Angle θ is measured from the normal to the force direction or vice versa as stated.

Concept / Approach:
Let the chosen axis be the normal direction. The projection of F onto that axis is F * cos θ when θ is the angle between F and the normal. If θ is defined from the tangential axis, then the normal component is F * sin θ; however, by the statement here (force inclined through θ° to the reference line with normal component needed), the standard interpretation yields the cosine factor for the component perpendicular to the line.

Step-by-Step Solution:
Construct a right triangle with hypotenuse F and included angle θ to the normal.Normal component = adjacent side = F * cos θ.Tangential component = opposite side = F * sin θ.

Verification / Alternative check:
At θ = 0°, the entire force is normal: F * cos 0° = F, consistent. At θ = 90°, normal component is zero: F * cos 90° = 0, also consistent.

Why Other Options Are Wrong:

• F * sin θ: This is the tangential component (if θ is to the normal).
• F * tan θ, F * sin θ * cos θ, F * sin^2 θ: Not simple projections; dimensionally or conceptually incorrect as a component magnitude.

Common Pitfalls:
Mixing angle definitions; forgetting which side of the right triangle corresponds to the component sought.

Final Answer:
F * cos θ