A man is dragging a trunk up the loading ramp of a mover's truck. The ramp has a slope angle of 20.00, and the man pulls
upward with a force of magnitude 375 N whose direction makes
an angle of 30.0° with the ramp. Find the horizontal and vertical
components of the force F.

The vertical component of the force is  187.5 N  and the horizontal component of the force is  324.8 N.

A vector is a any quantity that has both magnitude and direction. We can resolve any vector into its vertical and horizontal components. The vertical component of a vector such as force is F sin θ while the horizontal component of the force is F cos θ.

Given the following information from the question;

F =  375 N

θ = 30.0°

Vertical component(Fy) = 375 N sin 30.0° = 187.5 N

Horizontal component (Fx) = 375 N cos 30.0° = 324.8 N

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Horizontal component = 241 N

Vertical component =  287 N

Explanation:

Given:

Force =  F = 375 N

Referring to diagram attached, the force F is making an angle

theta = 20+30 = 50 with the horizontal.

Horizontal component = F*cos(theta) = 375*0.64278 = 241 N

Vertical component = F*sin(theta) = 375*0.76604 = 287 N