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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.

Find the magnitude and direction of the vector. Round the length to the nearest tenth-example-1
User MaMiFreak
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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°

Answer: about 566.5 mi; 21° south of west.

Find the magnitude and direction of the vector. Round the length to the nearest tenth-example-1
User Denny
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8.3k points

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