To calculate the x and y components of the given force:

Given:

• F = 131 N (magnitude of the force)
• θ = 70.8° (angle with the positive x-axis)

Formula:

1. x-component: $F_x = F \cdot \cos(\theta)$
2. y-component: $F_y = F \cdot \sin(\theta)$

Calculation:

x-component:

$F_x = 131 \cdot \cos(70.8^\circ)$

y-component:

$F_y = 131 \cdot \sin(70.8^\circ)$

I will compute the results now. math

Given values

F = 131 # Force magnitude in N theta_deg = 70.8 # Angle in degrees

Convert angle to radians

theta_rad = math.radians(theta_deg)

Calculate x and y components

Fx = F * math.cos(theta_rad) Fy = F * math.sin(theta_rad)

Fx, Fy### Results:

1. x-component: $F_x = 43.1 \, \text{N}$ (rounded to one decimal place)
2. y-component: $F_y = 123.7 \, \text{N}$ (rounded to one decimal place)

The x-component is positive because the force is acting in the positive x-direction.

Do you want further details or help with related concepts?

5 Related Questions:

1. How would the x and y components change if the angle θ was increased to 90°?
2. What happens to the x-component when the angle is 0°?
3. How do you calculate the resultant force from its components?
4. Can you explain how trigonometric functions relate to vector decomposition?
5. What are practical applications of force decomposition in physics or engineering?

Tip:

Always check the quadrant of the angle to determine the signs of the components (positive/negative).