Find the magnitude and direction of the vector. round the length to the nearest tenth and the degree to the nearest unit. diagram is not drawn to scale.

Refer to the diagram shown below.

The vector has a magnitude of a and a direction of θ degrees south of west. 

Use the Pythagorean Theorem to calculate a.
a² = (-530)² + (-200)² = 320900
a = √(320900) = 566.48 mi ≈ 566.5 mi

By definition,
tan θ = (-200)/(-530) = 0.3774
θ = tan⁻¹ 0.3774 = 20.68° ≈ 21°

about 566.5 mi; 21° south of west.