Answer:
75.5°
Explanation:
If we say F₁ is horizontal (0°), and F₂ is at angle θ, then the components are:
F₁ₓ = 2
F₁ᵧ = 0
F₂ₓ = 3 cos θ
F₂ᵧ = 3 sin θ
So the components of the resultant vector are:
Rₓ = 2 + 3 cos θ
Rᵧ = 3 sin θ
We know the magnitude of R, so using Pythagorean theorem:
4² = (2 + 3 cos θ)² + (3 sin θ)²
16 = 4 + 12 cos θ + 9 cos² θ + 9 sin² θ
16 = 4 + 12 cos θ + 9
3 = 12 cos θ
cos θ = 1/4
θ ≈ 75.5°
Alternatively, you can draw a diagram and use law of cosine to find the internal angle, then subtract from 180 to find θ.
