Answer:
21.21 N @ 81.87°
Explanation:
Divide each force into horizontal components and vertical components.
F₁ is in the +x direction, so F₁ₓ = 12 N and F₁ᵧ = 0 N.
F₂ is in the +y direction, so F₂ₓ = 0 N and F₂ᵧ = 9 N.
F₃ is 53.13° above the -x axis. So the components are:
F₃ₓ = -15 cos (53.13°) = -9 N
F₃ᵧ = 15 sin (53.13°) = 12 N
The horizontal component of the resultant force is the sum of the horizontal components of the individual forces:
Fₓ = F₁ₓ + F₂ₓ + F₃ₓ
Fₓ = 12 N + 0 N + (-9 N)
Fₓ = 3 N
Similarly, the vertical component of the resultant force is the sum of the vertical components of the individual forces:
Fᵧ = F₁ᵧ + F₂ᵧ + F₃ᵧ
Fᵧ = 0 N + 9 N + 12 N
Fᵧ = 21 N
To find the magnitude of the resultant force, use Pythagorean theorem:
F² = Fₓ² + Fᵧ²
F² = (3 N)² + (21 N)²
F = 21.21 N
To find the direction relative to the +x axis, use trigonometry:
tan θ = Fᵧ / Fₓ
tan θ = (21 N) / (3 N)
θ = 81.87°
The resultant force is 21.21 N at a angle of 81.87° above the +x axis (round as needed).
