Write each force in component form:
v ₁ : 50 N due east → (50 N) i
v ₂ : 80 N at N 45° E → (80 N) (cos(45°) i + sin(45°) j ) ≈ (56.5 N) (i + j )
The resultant force is the sum of these two vectors:
r = v ₁ + v ₂ ≈ (106.5 N) i + (56.5 N) j
Its magnitude is
|| r || = √[(106.5 N)² + (56.5 N)²] ≈ 121 N
and has direction θ such that
tan(θ) = (56.5 N) / (106.5 N) → θ ≈ 28.0°
i.e. a direction of about E 28.0° N. (Just to clear up any confusion, I mean 28.0° north of east, or 28.0° relative to the positive x-axis.)
